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[ "# Q.7 In a class test containing 10 questions, 5 marks are awarded for every correct answer and (-2) marks are awarded for every incorrect answer and 0 for questions not attempted. (i) Mohan gets four correct and six incorrect answers. What is his score? (ii) Reshma gets five correct answers and five incorrect answers, what is her score? (iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?\n\n(i) Awarded for correct answer =(4×5) marks\nAwarded for incorrect answer =6× (-2) marks\nTotal marks obtained by Mohan\n= (4×5)+{6× (-2)}= 20-12=8\n(ii) Awarded for correct answer = 5×5 = 25 Marks\nAwarded for incorrect answer = 5 ×(-2) = -10\nTotal Marks obtained by Reshma =25-10 = 15 marks\n(iii) Awarded for correct answer = 2×5 = 10Marks\nAwarded for incorrect answer = 5×(-2) = -10\nTotal Marks obtained by Reshma =10-10= 0marks" ]

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[ "# Bearing remaining life prediction using Gaussian process regression with composite kernel functions\n\n## Sheng Hong1, Zheng Zhou2, Chen Lu3, Baoqing Wang4, Tingdi Zhao5\n\n1, 3, 4, 5Science and Technology on Reliability and Environmental Engineering Laboratory, School of Reliability and System Engineering, Beihang University, Beihang, China\n\n2Systems Engineering Research Institute, China State Shipbuilding Corporation (CSSC), Beijing, China\n\n1, 3Corresponding authors\n\nJournal of Vibroengineering, Vol. 17, Issue 2, 2015, p. 695-704.\nReceived 20 March 2014; received in revised form 30 January 2015; accepted 20 February 2015; published 31 March 2015\n\nCopyright © 2015 JVE International Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.\nViews 664\nAbstract.\n\nThere is an urgent demand for life prediction of bearing in industry. Effective bearing degradation assessment technique is beneficial to condition based maintenance (CBM). In this paper, Gaussian Process Regression (GPR) is used for remaining bearing life prediction. Three main steps of prediction schedule are presented in details. RMS, Kurtosis and Crest factor are used for feature fusion by self-organizing map (SOM). Minimum Quantization Error (MQE) value derived from SOM is applied to represent the condition of bearing. GPR models with both single and composite covariance functions are presented. After training, new MQE value can be predicted by the GPR model according to previous data points. Experimental results show that composite kernels improve the accuracy and reduce the variance of prediction results. Compared with particle filter (PF), GPR model can predict the remaining life of bearings more accurately.\n\nKeywords: Gaussian process regression, uncertainty distribution, bearing life prediction.\n\n#### 1. Introduction\n\nBearings are the most widely used mechanical and rotational parts in industrial equipments . In order to avoid the fatal breakdowns of machines caused by unexpected failures, defects of bearings should be detected as early as possible . Condition based maintenance (CBM) which can reduce the cost of maintenance, becomes an efficient strategy for modern industry these years . Effective prediction of bearing remaining life is important to identify the future conditions for maintenance plans, thus can reduce the downtime, maintenance cost and safety hazards .\n\nBearing performance prognostics means forecasting the remaining useful life (RUL) or future condition of equipment based on the acquired condition monitoring data. Although studies on prognostics of bearing RUL have received much attention recent years, the accurate estimation of the RUL of bearing is still challenging. Data-driven methods predict the results according to the historical records and the condition monitoring (CM) data. Vibration signal is effective to reflect the running condition of bearings . Three major steps are crucial to achieve failure prediction result. Firstly, degradation indicator should be selected properly. Secondly, the degradation of machine should be tracked and assessed continuously. Finally, RUL of machine should be effectively predicted according to the monitoring data.\n\nPrognostics algorithm is crucial to the effectiveness of failure prediction. Many popular prediction models have already been applied in the literatures. Artificial Neural Network (ANN) which has good self-learning and adaptive ability, is widely used in these prognostics models. In , Feed Forward Neural Network (FFNN) was used to achieve more accurate estimation of the RUL of bearings. Reference proposed a recurrent wavelet neural network (RWNN) to predict the crack propagation of rolling bearings. Meanwhile, some new non-linear prognostics methods have also been employed to forecast RUL. For example, in , SVM-based model was developed to compute the ratio of bearing running time to failure time. In , a combination of logistic regression (LR) and relevance vector machine (RVM) was used to assess the health state and failure time.\n\nThese models work perfectly for some particular scenes. However, fewer machine learning methods can provide the probability density function (PDF) of RUL, which is important to handle the uncertainty problem. The probability indication of the predicted results is important to make maintenance decisions and risk analysis . Sankalita Saha proposed a distributed GPR-based prognostics algorithm to predict battery RUL with an uncertainty management. The results showed that GPR is superior to particle filters (PF) for battery prognostics.\n\nGPR is a new promising technique which has received much attention in the machine-learning field over the past years. Due to the advantages in uncertainty predictions, GPR provides a good adaptability to handle nonlinear, complex classification and regression problems. Compared with artificial neural network, GPR is simpler to understand and implement in practice. Kernel functions in GPR models are similar with support vector regression (SVR) and relevance vector machines (RVM). However, GPR provides probabilistic outputs, by an uncertainty interval for the input data. Thus, GPR is being applied to various engineering problems with uncertainty.\n\nAiming to achieve an accurate failure prediction of bearing, a data-driven model based on GPR is proposed in this paper. A failure prediction model is constructed based on GPR with different covariance functions after feature extraction and fusion. The training input of this model is from bearings’ run-to-failure experiment.\n\nThe rest of the paper is organized as follows. In Section 2, GPR method is introduced detailedly. The bearing failure prediction model based on GPR is described in Section 3. In Section 4, applications of the proposed method are presented with experiment data. Finally, the conclusions are made in Section 5.\n\n#### 2. Principle of GPR\n\nGPR is one of the most important Bayesian machine learning approaches . As a probabilistic technique for nonlinear regression, it computes the posterior degradation estimates by constraining the priori distribution to fit the available training data.\n\nGaussian Process (GP) is a random process. It is defined as a series of random variables with any finite number of which has a joint Gaussian distribution. A GP is completely specified by its mean function $\\mu \\left(x\\right)$ and covariance function , which can be defined as:\n\n(1)\n$f\\left(x\\right)~GP\\left(\\mu \\left(x\\right),C\\left(x,{x}^{\\text{'}}\\right)\\right),$\n(2)\n$\\mu \\left(x\\right)=E\\left[f\\left(x\\right)\\right],$\n(3)\n$C\\left(x,{x}^{\\text{'}}\\right)=E\\left[\\left(f\\left(x\\right)-\\mu \\left(x\\right)\\right)\\left(f\\left({x}^{\\text{'}}\\right)-\\mu \\left({x}^{\\text{'}}\\right)\\right)\\right],$\n\nwhere are random variables.\n\nGiven priori information about the GP and a set of training points ($n$ is dataset number), the posterior distribution is derived by imposing a restriction on joint priori distribution . A GP model with noise is defined as:\n\n(4)\n${y}_{i}=f\\left({x}_{i}\\right)+\\epsilon ,$\n\nwhere $\\epsilon$ is additive Gaussian noise $N\\left(0,{\\sigma }^{2}\\right)$.\n\nFor a new test input ${x}^{*}$, we can establish a joint Gaussian priori distribution of the training output y and the test output ${y}^{*}$ as follows:\n\n(5)\n$\\left[\\begin{array}{c}y\\\\ {y}^{*}\\end{array}\\right]~N\\left(0,\\left[\\begin{array}{cc}C\\left(X,X\\right)+{\\sigma }_{n}^{2}I& C\\left(X,{x}^{*}\\right)\\\\ C\\left(X,{x}^{*}\\right)& C\\left({x}^{*},{x}^{*}\\right)\\end{array}\\right]\\right),$\n\nwhere $C\\left(X,X\\right)$ is $n$-order symmetric positive definite covariance matrix, $C\\left(X,{x}^{*}\\right)$ is the $n\\text{×1}$ covariance matrix of the test input ${x}^{*}$ and the training input $X$, and $C\\left({x}^{*},{x}^{*}\\right)$ is the covariance matrix of the test input ${x}^{*}$. Under the conditions of a given input ${x}^{*}$ and the training set $D$, the GP can calculate the test output ${y}^{*}$ according to the posterior probability formula as follows:\n\n(6)\n${y}^{*}|{x}^{*},D~N\\left({\\mu }_{{y}^{*}},{\\sigma }_{{y}^{*}}^{2}\\right),$\n(7)\n${\\mu }_{{y}^{*}}=C\\left({x}^{*},X\\right){\\left(C\\left(X,X\\right)+{\\sigma }_{n}^{2}I\\right)}^{-1}y=\\sum _{i=1}^{n}{\\alpha }_{i}C\\left({x}^{i},{x}^{*}\\right),$\n\nwhere ${\\mu }_{{y}^{*}}$, ${\\sigma }_{{y}^{*}}$ are expectation and variance of ${y}^{*}$ and $\\alpha ={\\left(C+{\\sigma }_{n}^{2}I\\right)}^{-1}y$, where $I$ is unit matrix.\n\nThe predicted mean value is a linear combination of covariance functions according to Eq. (7). A crucial ingredient in a Gaussian process predictor is the covariance function that encodes the assumptions about the functions to be learnt by defining the relationship between data points. Once a posterior distribution is obtained, it can be used to predict values for the test data points.\n\nThree single covariance functions are used in this study, namely squared exponential (SE) covariance function, rational quadratic (RQ) covariance function and Matern class of covariance functions [12, 13]. These covariance functions are described as follows.\n\n1) The squared exponential (SE) covariance function:\n\n(8)\n${C}_{SE}\\left({x}^{i},{x}^{j}\\right)={\\sigma }_{f}^{2}\\mathrm{e}\\mathrm{x}\\mathrm{p}\\left(-\\frac{{{\\left(x}^{i}-{x}^{j}\\right)}^{2}}{{2l}^{2}}\\right).$\n\n2) The rational quadratic (RQ) covariance function:\n\n(9)\n\n3) The Matern class of covariance functions:\n\n(10)\n${C}_{M}\\left({x}^{i},{x}^{j}\\right)={\\sigma }_{f}^{2}\\left[1+\\sqrt{3M}{\\left(x}^{i}-{x}^{j}\\right){e}^{\\sqrt{3M}{\\left(x}^{i}-{x}^{j}\\right)}\\right],$\n\nwhere $\\alpha$, $l$, ${\\sigma }_{f}^{2}$, $M$ are hyper-parameters, and the $i$ and $j$ represent the $i$-th and the $j$-th vector in the input matrix $X$.\n\nIn order to predict the remaining life of bearing, GPR requires a priori knowledge about the form of covariance function. The choice of covariance function must be specified by users, and the corresponding hyper-parameters can be learnt from the training data. The parameters are optimized by maximizing the marginal likelihood algorithm , as shown in the following:\n\n(11)\n$L=\\mathrm{lg}\\left[p\\left(y|X,\\theta \\right)\\right]=-\\frac{1}{2}{y}^{T}{Q}^{-1}y-\\frac{1}{2}\\mathrm{lg}\\left|Q\\right|-\\frac{n}{2}\\mathrm{lg}\\left(2\\pi \\right),$\n(12)\n$\\frac{\\partial }{\\partial {\\theta }_{i}}\\mathrm{lg}\\left[p\\left(y|X,\\theta \\right)\\right]=\\frac{1}{2}\\mathrm{t}\\mathrm{r}\\left[\\left(\\alpha {\\alpha }^{T}-{Q}^{-1}\\right)\\frac{\\partial Q}{\\partial {\\theta }_{i}}\\right],$\n\nwhere is a vector containing all hyper-parameters, and $Q=C+{\\sigma }_{n}^{2}I$ is the covariance matrix for the noisy target $y$.\n\n#### 3. Remaining life prediction for bearings using GPR\n\nIn this section, the remaining life prediction model is presented. The schematic diagram of the proposed model is shown in Fig. 1.\n\n#### 3.1. Feature extraction\n\nMost mechanical failures can be represented by the feature of vibration signal. After feature extraction, several time-domain features can be obtained to assess the health state of the bearing and predict the RUL . Three features are used in the proposed model, i.e. RMS, Kurtosis and Crest factor . These features can be calculated as follows:\n\n(13)\n$Kurtosis=\\frac{{\\sum }_{k=1}^{K}{\\left(x\\left(k\\right)-{x}_{m}\\right)}^{4}}{K{x}_{std}^{4}},$\n(14)\n$RMS={X}_{RMS}=\\sqrt{\\frac{\\sum _{k=1}^{K}{\\left(x\\left(k\\right)\\right)}^{2}}{K}},$\n(15)\n$Crest=\\frac{{X}_{PEAK}}{{X}_{RMS}},$\n\nwhere $x\\left(k\\right)$ is a series of vibration signal for $k=$ 1, 2,…, $K$, and $K$ is the number of data points, and ${X}_{PEAK}$ is the maximum value of signal series.These features are usually stable under the normal condition, whereas they obviously change once bearings degrade. The three features are sensitive to different types of failures and the combination of them are more effective in performance assessment.\n\nFig. 1. Schematic diagram of the proposed prediction method", null, "#### 3.2. Feature fusion by SOM\n\nSOM is a kind of neural network . It can form two-dimensional indicator from multi-dimensional data. Each neuron of the SOM is represented by an $n$-dimensional weight vector ${m}_{i}={\\left({m}_{i1},{m}_{i2},\\dots ,{m}_{in}\\right)}^{T}$ . The neurons of the map are connected to adjacent neurons by a neighborhood relation. RMS, kurtosis and crest are combined as the input $X$. Then the SOM network is trained iteratively by the input under normal condition. For a new vector input $T$, the neuron whose weight vector is the closest to the input vector is called the best matching unit (BMU), which is defined as follows:\n\n(16)\n$\\left|\\left|x-{m}_{BMU}\\right|\\right|=\\underset{i}{\\mathrm{m}\\mathrm{i}\\mathrm{n}}\\left\\{\\left|\\left|x-{m}_{i}\\right|\\right|\\right\\}.$\n\nDuring the training procedure, the weight vectors of BMU are updated as well as its topological neighbors by the following learning rule:\n\n(17)\n${m}_{i}\\left(t+1\\right)={m}_{i}\\left(t\\right)+a\\left(t\\right)h\\left({n}_{BMU},{n}_{i},t\\right)\\left[X-{m}_{i}\\left(t\\right)\\right],$\n\nwhere $\\left({n}_{BMU},{n}_{i},t\\right)$ is the neighborhood function, $\\alpha \\left(t\\right)$ is the learning rate. The distance between the BMU and the test input data $T$ is called the minimum quantization error (MQE) . Thus, the degradation condition can be represented by the MQE as follows:\n\n(18)\n$MQE=\\left|\\left|T-{m}_{BMU}\\right|\\right|,$\n\nwhere $T$ is the test input data vector and ${m}_{BMU}$ stands for the weight vector of BMU.\n\n#### 3.3. Failure threshold\n\nThe bearing health state during the whole bearing life is divided into three stages as normal, degradation and failure. After sampling from bearing vibration data, we calculate the three features into MQE value and then compare the incipient failure thresholds. The normal value of MQE is in range of 0-0.3. Therefore, the incipient threshold is set as 0.3 and the failure threshold is set as 1.0. If the features exceed the incipient threshold and enter the degradation area, an incipient fault will occur. And then the prediction model will be activated to continually track and record the vibration data. Once the failure threshold is exceeded, bearing suffers from a severe degradation and must be replaced.\n\nA multistep prediction method is used in this paper. The initial time step is a very important element in bearing remaining life prediction. In order to realize the bearing remaining life prediction, the initial time step should be a point whose MQE is below the failure threshold. Generally, we choose the initial time step with a MQE value between the incipient failure threshold (the value is 0.3 in thise paper) and the final failure threshold (the value is 1 in thise paper). However, different initial time step result in different prediction accuracy.\n\n#### 3.4. GPR prediction\n\nGPR is used to predict the failure time of bearings by assessing the features of bearings. The hyper-parameters are obtained by maximizing the marginal likelihood algorithm . The model outputs the predicted MQE value and confidence interval for the next steps. The latest $k$ (in this paper, $k=$ 10) MQEs are took as input vector of GPR to predict the next several periods. The RUL of the bearing can be obtained based on the predicted MQE and failure threshold.\n\nCovariance function is a key factor in GPR. Three standard covariance functions are used in this paper (i.e. squared exponential (SE) covariance function, rational quadratic (RQ) covariance function and Matern class of covariance functions). If ${f}_{1}\\left(x\\right)$, ${f}_{2}\\left(x\\right)$,…, are independent random GP, $f\\left(x\\right)=\\sum _{i=1}^{n}{f}_{i}\\left(x\\right)$ is also a GP. Therefore, a composite covariance function can be described as:\n\n(19)\n${C}_{CK}\\left({x}^{i},{x}^{j}\\right)=\\sum _{i=1}^{n}{C}_{i}\\left({x}^{i},{x}^{j}\\right).$\n\nFig. 2. Bearing test rig sensor placement illustration", null, "a)", null, "b)\n\n#### 4. Case studies\n\nIn this section, we used the test data of bearing to validate the effectiveness of the proposed bearing failure prediction model. The bearing test dataset was generated from the run-to-failure test performed under a constant load condition by the national science foundation industry and university corporative research program (NSF I/UCR) center on Intelligent Maintenance Systems (IMS). The test rig is shown in Fig. 2.\n\nFour bearings were installed on one shaft for the run-to-failure test [18, 19]. The rotation speed was maintained at 2000 rpm. A radial load of 2730 kg was placed onto the shaft and the bearings by a spring mechanism. Vibration data were collected every 20 minutes, with a sampling rate of 20 kHz. Three tests were carried out and all tests were terminated when some failure occurred.\n\nIn order to give a brief demonstration of the proposed method, a part of MQEs were shown in Fig. 3. Three time domain features are applied to construct the input vector of SOM. After training SOM, the MQE of each test dataset can be calculated by Eq. (13)-(15).\n\nFig. 3. MQE of test bearing", null, "#### 4.1. Prediction based on GPR\n\nSeveral degradation datasets are extracted from Bearing 3 of Test 1 and used to make predictions. Performance degradation causes fluctuation of bearing vibration and the increase of MQE. When MQE exceeds the incipient threshold, the prediction model are activated. If MQE exceeds 1.0, bearing enters the failure stage and should be replaced.\n\nThe evolution of MQE of the vibration signal of bearing 3 with threshold setting and prediction is shown in Fig. 4. The prediction is trigged at the 40th time step, where the MQE is about 0.7. The dotted line is the actual MQE and the solid line indicates the prediction result of GPR with composite covariance function. The actual failure time is 55.3 and the predicted one is 56.6. The prediction is overestimated with an accuracy of 97.7 %, which is acceptable.\n\nFig. 4. Remaining life prediction for bearing MQE", null, "The prediction model based on GPR (CK) with 95 % confidence interval is used, as depicted in Fig. 5. Three prediction processes were triggered at the 30th, 40th and 52th time step, respectively. The corresponding MQEs of the bearing are approximately equal to 0.5, 0.7 and 0.9, respectively. The lines represent the predicted MQEs and the colored areas are the uncertainty areas of the predicted results. Among these lines, the black dot one indicates the actual MQE. It can be found that the predictions at 30 failed to follow the actual trend. Thus, prediction at the early stage faces a larger deviation. While, with more new data being added, the predictions become better as illustrated by the predictions at 40 and 52.\n\nFig. 5. Prediction of MQE based on GPR (CK) with 95 % confidence interval at 30, 40 and 52", null, "#### 4.2. Comparisons between different kernels\n\nCovariance function is crucial for GPR, and can determine the efficiency of prediction. In this case, 60 points were used to make a comparison between different kernels. The length of the training data are 10. Six covariance functions are applied to the prediction model for training and validation. As shown in Fig. 6, most of kernels can suit the actual data well for one-step prediction. The RMS error (RMSE) and output variance are used to estimate the accuracy. Although, composite covariance functions consumed more time, they exhibited better performance (smaller RMSE and variance) than the single kernels. As listed in Table 1, the RMSE of the composite kernel of SE and Matern is smaller than others. Variance also reduces significantly. The composite kernel spent additional 60 % computing time in exchange for 30 % performance enhancement, which is valuable.\n\nFig. 6. Predictions with different covariance functions", null, "For an $n$-steps prediction, the dynamic of PDF predictions with single and composite covariance functions is shown in Fig. 7. The RUL distributions of both kernels cover the real RULs well. However, the distributions of RUL obtained from the single kernel have a larger PDF at early time, which means the variance of prediction is higher than the composite covariance functions. More accurate prediction with higher confidence can be obtained at the end life. This probabilistic implement help us make a correct judgment and provide an uncertainty management.\n\nFig. 7. PDF of prediction with different covariance functions", null, "Table 1. Comparison of different kernels\n\n Kernel RMSE Variance Computing time SE 0.0357 0.08307 0.6738 RQ 0.0358 0.08290 0.9120 Matern 0.0351 0.08396 0.6930 SE+RQ 0.0197 0.03158 1.4845 SE+ Matern 0.0195 0.03515 1.0655 RQ+Matern 0.0190 0.03327 1.4503\n\n#### 4.3. Comparison with particle filter\n\nPF is a kind of Sequential Monte Carlo (SMC) methods that are coupled with the recursive Bayesian estimation . The principle of PF is to utilize a set of weighted particles to represent the probability densities. 120 points degradation data are used to make a comparison. The failure threshold of the MQE is set as 1.0. The predictions are started at 100th time step. Both PF and GPR prediction model are run ten times and the average results are calculated. Fig. 8(a) is the prediction result using PF, and Fig. 8(b) is the prediction using GPR with the composite kernel.\n\nFig. 8. Comparison of MQE prediction between composite kernel GPR and PF method", null, "a)", null, "b)\n\nThe actual failure time as shown in the Fig. 8 is 116.2. While the mean value of the predicted failure time by GPR and PF are 117.8 and 119.1 respectively. Both results are acceptable. Compared with PF, GPR has a better accuracy and the predicted curve of GPR is more stable. That is to say GPR is superior to PF in maintenance decision.\n\n#### 5. Conclusions\n\nThis paper proposes a bearing remaining life prediction model based on GPR with composite kernel. Dynamic of PDF is illustrated in the experiment. The PDF of model outputs is essential for risk analysis and maintenance decision. From this paper, following conclusions can be drawn:\n\n1) This paper proposes a creative application of GPR in bearing prediction field. The GPR model can simplify the prediction process with a satisfactory performance.\n\n2) GPR with composite kernels can improve the prediction accuracy and reduce the variance of the RUL in comparison with single kernel.\n\n3) Compared with PF algorithm, GPR model is better in terms of prediction accuracy.\n\n#### Acknowledgements\n\nThe authors are highly thankful for the financial support of National Natural Science Foundation of China (61304111), Beijing Natural Science Foundation (4153059), National Program on Key Basic Research Program of China under Grant 2014CB744904, and Fundamental Research Funds for the Central Universities under Grant No. YWF-14-KKX-001, China.\n\n1. Heng A., Zhang S., Tan A. C. C. Rotating machinery prognostics: State of the art, challenges and opportunities. Mechanical Systems and Signal Processing, Vol. 23, Issue 3, 2009, p. 724-739. [Search CrossRef]\n2. Qiu H., Lee J., Lin J. Robust performance degradation assessment methods for enhanced rolling element bearing prognostics. Advanced Engineering Informatics, Vol. 17, Issue 3, 2003, p. 127-140. [Search CrossRef]\n3. Pan Y., Chen J., Guo L. Robust bearing performance degradation assessment method based on improved wavelet packet-support vector data description. Mechanical Systems and Signal Processing Vol. 23, Issue 3, 2009, p. 669-681. [Search CrossRef]\n4. Huang R., Xi L., Li X., Richard C., Qiu H., Lee J. Residual life predictions for ball bearings based on self-organizing map and back propagation neural network methods. Mechanical Systems and Signal Processing, Vol. 21, Issue 1, 2007, p. 193-207. [Search CrossRef]\n5. Gebraeel N., Lawley M., Liu R. Residual life predictions from vibration-based degradation signals: a neural network approach. IEEE Transactions on Industrial Electronics, Vol. 51, Issue 3, 2004, p. 694-700. [Search CrossRef]\n6. Mahamad A. K., Saon S., Hiyama T. Predicting remaining useful life of rotating machinery based artificial neural network. Applied Mathematics and Computation, Vol. 60, Issue 4, 2010, p. 1078-1087. [Search CrossRef]\n7. Wang P., Vachtsevanos G. Fault prognostics using dynamic wavelet neural networks. Ai Edam-Artificial Intelligence for Engineering Design Analysis and Manufacturing, Vol. 15, Issue 4, 2001, p. 349-365. [Search CrossRef]\n8. Sun C., Zhang Z., He Z. Research on bearing life prediction based on support vector machine and its application. Journal of Physics: Conference Series, Vol. 305, Issue 1, 2011, p. 12-28. [Search CrossRef]\n9. Caesarendra W., Widodo A., Yang B. Application of relevance vector machine and logistic regression for machine degradation assessment. Mechanical Systems and Signal Processing, Vol. 24, Issue 4, 2010, p. 1161-1171. [Search CrossRef]\n10. Saha S., Saha B., Goebel K. A distributed prognostic health management architecture. Proceedings of the Conference of the Society for Machinery Failure, 2009. [Search CrossRef]\n11. Saha S., Saha B., Saxena A., Goebel K. Distributed prognostic health management with gaussian process regression. IEEE Aerospace Conference, 2010, p. 1-8. [Search CrossRef]\n12. Liu K., Liu B., Xu C. Intelligent analysis model of slope nonlinear displacement time series based on genetic-Gaussian process regression algorithm of combined kernel function. Chinese Journal of Rock Mechanics and Engineering, Vol. 10, 2009, p. 2128-2134. [Search CrossRef]\n13. Rasmussen C. E., Williams C. K. I. Gaussian Processes for Machine Learning. MIT Press Cambridge, MA, 2006. [Search CrossRef]\n14. Mortada M., Yacout S., Lakis A. Diagnosis of rotor bearings using logical analysis of data. Journal of Quality in Maintenance Engineering, Vol. 17, Issue 4, 2011, p. 371-397. [Search CrossRef]\n15. Hong S., Zhou Z., Zio E., Hong K. Condition assessment for the performance degradation of bearing based on a combinatorial feature extraction method. Digital Signal Processing, Vol. 27, 2014, p, 159-166. [Search CrossRef]\n16. Kohonen T. Self-Organizing Maps. Springer, 1995. [Search CrossRef]\n17. Jamsa-Jounela S., Vermasvuori M., Enden P., Haavisto S. A process monitoring system based on the Kohonen self-organizing maps. Control Engineering Practice, Vol. 11, Issue 1, 2003, p. 83-92. [Search CrossRef]\n18. Lee J., Qiu H., Yu G., Lin J. Bearing Data Set. IMS, University of Cincinnati. NASA Ames Prognostics Data Repository, NASA Ames, Moffett Field, CA, http://ti.arc.nasa.gov/project/prognostic-data-repository. [Search CrossRef]\n19. Hong S., Wang B., Li G.,Hong Q. Performance degradation assessment for bearing based on ensemble empirical mode decomposition and gaussian mixture model. Journal of Vibration and Acoustics, Vol. 136, Issue 6, 2014, p. 061006. [Search CrossRef]\n20. Doucet A., Godsill S., Andrieu C. On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, Vol. 10, Issue 3, 2000, p. 197-208. [Search CrossRef]" ]

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[ "# Long Short-Term Memory Music Composer\n\nAutomatic Music Composition", null, "For almost as long as I have been able to program I have wanted to create software that could compose music.\n\nI have had some primitive attempts at automated music composition over the years in Visions of Chaos. Mostly based on simple math formulas or genetic mutations of random note sequences. After recently having some success learning and implementing TensorFlow and neural networks for cellular automata searching I was keen to try using neural networks for music creation.\n\nHow It Works\n\nThe composer works by training a long short-term memory (LSTM) neural network. LSTM networks are good at predicting “what comes next” in a sequence of data. Another page that goes into more depths about LSTMs is here.", null, "The LSTM network is fed a bunch of different note sequences (in this case single channel midi files). Once the network has been trained sufficiently it is then able to create music that is similar to the training material.", null, "The above diagrams of LSTM internals may look daunting, but using TensorFlow and/or Keras makes creating and experimenting with LSTMs much simpler.\n\nSource Music to Train Model\n\nFor these simpler LSTM composer networks you want source songs with just a single midi channel. Solo piano midi files work well for this. I found single piano midi files at Classical Piano Midi Page and mfiles that I used for training my models.\n\nMusic of different composers is put into separate folders. That way the user can select Bach, click the Compose button and have a piece of music generated that (hopefully) sounds a little like Bach.\n\nLSTM Model\n\nThe model I based my code on was this example by Sigurður Skúli Sigurgeirsson which he describes in more detail here.\n\nI ran the included lstm.py script and after 15 hours it had finished training. When I used the predict.py to generate midi files they all disappointingly contained just a repeated single note. I reran it two times more and got the same results.\n\nThe original model is\n\n``````\nmodel = Sequential()\nmodel.compile(loss='categorical_crossentropy', optimizer='rmsprop',metrics=[\"accuracy\"])\n```\n```\n\nOnce I had plotting added to the script I saw why the model does not work.", null, "The accuracy never rises as it should over time and the loss gets stuck at around 3.4 because of this. See the good plots further down this post to see what the accuracy plot should like look in a working model.\n\nI have no idea why, but I gave up on that model and started tweaking settings.\n\n``````\nmodel = Sequential()\n```\n```\n\nSmaller and fewer LSTM layers. I added BatchNormalization too after seeing it in a sentdex video. There are most likely better models, but this one worked OK for the rest of my training sessions.\n\nNote that in both models I have replaced LSTM with CuDNNLSTM. This results in much faster LSTM training by using Cuda. If you do not have a Cuda capable GPU you would need to change these back to LSTM. Thanks to sentdex for this tip. Training new models and composing midi files is approximately 5 times as fast using CuDNNLSTM.\n\nHow Long Should You Train Your Model For\n\nDepending on how long you train the model (how many epochs) determines how similar to the source music the results will be. Too few epochs and the output will have too many repeated notes. Too many epochs and the model will overfit and just copy the source music.\n\nBut how do you know how many epochs to stop at?\n\nA simple method is to add a callback that saves the model and a plot of accuracy and loss every 50 epochs during a 500 epoch training run. That way, once the training is done you have 50 epoch increment models and graphs that show you exactly how the training is going.\n\nHere are the graph results from a sample run saving every 50 epochs merged into an animated GIF file.", null, "That is the sort of graph you want to see. Loss should drop down and stay down. Accuracy should rise and stay up near 100%.\n\nYou want to use a model with the epoch count corresponding to when the graphs first hit their limits. For the above graph this would be 150 epochs. Using any of the models beyond this would be using a model trained too long and most likely result in a model that just copies the source material.\n\nThe model those graphs are showing was trained on the “Anthems” midi files from here.", null, "Sample midi output from the 150 epoch model.", null, "Sample midi output from the 100 epoch model.\n\nEven the 100 epoch model may be copying the source too closely. This could be due to the relatively small sample of midi files to train against. The training works better with more total notes.", null, "The above is an example of what can and does happen sometimes during training. The loss is decreasing and accuracy increasing as they usually do and then suddenly they both crap out. At that point you may as well stop training. The model will not (at least from my experience) ever start training correctly again. In this case the saved 100 epoch model is too random and the 150 is just past the point the model failed. I am now saving every 25 epochs to be sure I get that sweet spot of the best trained model before it trains too much or fails.", null, "Another example of training failing. This model was trained on the midi files from here. In this case it was going good until just after epoch 200. Using the epoch 200 model gives the following Midi output.\n\nWithout plotting you never know when or if the training has problems and if you may be able to still get a good model without having to retrain from scratch.\n\nMore Examples", null, "75 epoch model based on Chopin.", null, "50 epoch model based on Christmas Midi files.", null, "100 epoch model based on Christmas Midi files. Not sure how “Christmasy” they sound?", null, "300 epoch model based on Bach Midi files from here and here.", null, "200 epoch model based on a single Balakirew Midi file from here.", null, "200 epoch model based on Debussy.", null, "175 epoch model based on Mozart.", null, "100 epoch model based on Schubert.", null, "200 epoch model based on Schumann.", null, "200 epoch model based on Tchaikovsky.", null, "175 epoch model based on folk songs.", null, "100 epoch model based on nursery rhymes.", null, "100 epoch model based on wedding music.", null, "200 epoch model based on my own midi files that come from my YouTube movies soundtracks. This may be overtrained slightly as it generates what is more of a medly of my short 1 or 2 bar midi files.\n\nSheet Music\n\nOnce you have the midi file, you can use online tools like SolMiRe to convert them into sheet music. The following is the 200 epoch Softology midi file above.", null, "", null, "Availability\n\nThe LSTM Composer is now included as part of Visions of Chaos.", null, "You select a style from a dropdown list and click Compose. As long as you have the Python and TensorFlow pre-reqs installed (see here for instructions), within seconds (if you have a fast GPU) you will have a new machine composed midi file to listen to and use for any other purpose. No copyright. No royalties need to be paid. If you don’t like the results you can click Compose again a few seconds later you will have a new composition to listen to.\n\nThe results so far could not be considered full songs, but they all do contain interesting smaller sequences of notes that I will be using when creating music in the future. In this way the LSTM composer can be a good inspiration starting point for new songs.\n\nPython Source\n\nHere are the LSTM training and prediction Python scripts I am using. You do not need to have Visions of Chaos installed for these scripts to work and the training and midi generation will both work from the command line.\n\nThis is the training script “lstm_music_train.py”\n\n``````\n# based on code from https://github.com/Skuldur/Classical-Piano-Composer\n# to use this script pass in;\n# 1. the directory with midi files\n# 2. the directory you want your models to be saved to\n# 3. the model filename prefix\n# 4. how many total epochs you want to train for\n# eg python -W ignore \"C:\\\\LSTM Composer\\\\lstm_music_train.py\" \"C:\\\\LSTM Composer\\\\Bach\\\\\" \"C:\\\\LSTM Composer\\\\\" \"Bach\" 500\n\nimport os\nimport tensorflow as tf\n\n# ignore all info and warning messages\nos.environ['TF_CPP_MIN_LOG_LEVEL'] = '2'\ntf.compat.v1.logging.set_verbosity(tf.compat.v1.logging.ERROR)\n\nimport glob\nimport pickle\nimport numpy\nimport sys\nimport keras\nimport matplotlib.pyplot as plt\n\nfrom music21 import converter, instrument, note, chord\nfrom datetime import datetime\nfrom keras.models import Sequential\nfrom keras.layers.normalization import BatchNormalization\nfrom keras.layers import Dense\nfrom keras.layers import Dropout\nfrom keras.layers import CuDNNLSTM\nfrom keras.layers import Activation\nfrom keras.utils import np_utils\nfrom keras.callbacks import TensorBoard\nfrom shutil import copyfile\n\n# name of midi file directory, model directory, model file prefix, and epochs\nmididirectory = str(sys.argv)\nmodeldirectory = str(sys.argv)\nmodelfileprefix = str(sys.argv)\nmodelepochs = int(sys.argv)\n\nnotesfile = modeldirectory + modelfileprefix + '.notes'\n\n# callback to save model and plot stats every 25 epochs\nclass CustomSaver(keras.callbacks.Callback):\ndef __init__(self):\nself.epoch = 0\n# This function is called when the training begins\ndef on_train_begin(self, logs={}):\n# Initialize the lists for holding the logs, losses and accuracies\nself.losses = []\nself.acc = []\nself.logs = []\ndef on_epoch_end(self, epoch, logs={}):\n# Append the logs, losses and accuracies to the lists\nself.logs.append(logs)\nself.losses.append(logs.get('loss'))\nself.acc.append(logs.get('acc')*100)\n# save model and plt every 50 epochs\nif (epoch+1) % 25 == 0:\nsys.stdout.write(\"\\nAuto-saving model and plot after {} epochs to \".format(epoch+1)+\"\\n\"+modeldirectory + modelfileprefix + \"_\" + str(epoch+1).zfill(3) + \".model\\n\"+modeldirectory + modelfileprefix + \"_\" + str(epoch+1).zfill(3) + \".png\\n\\n\")\nsys.stdout.flush()\nself.model.save(modeldirectory + modelfileprefix + '_' + str(epoch+1).zfill(3) + '.model')\ncopyfile(notesfile,modeldirectory + modelfileprefix + '_' + str(epoch+1).zfill(3) + '.notes');\nN = numpy.arange(0, len(self.losses))\n# Plot train loss, train acc, val loss and val acc against epochs passed\nplt.figure()\nplt.subplot(2, 1, 1)\n# plot loss values\nplt.plot(N, self.losses, label = \"train_loss\")\nplt.title(\"Loss [Epoch {}]\".format(epoch+1))\nplt.xlabel('Epoch')\nplt.ylabel('Loss')\nplt.subplot(2, 1, 2)\n# plot accuracy values\nplt.plot(N, self.acc, label = \"train_acc\")\nplt.title(\"Accuracy % [Epoch {}]\".format(epoch+1))\nplt.xlabel(\"Epoch\")\nplt.ylabel(\"Accuracy %\")\nplt.savefig(modeldirectory + modelfileprefix + '_' + str(epoch+1).zfill(3) + '.png')\nplt.close()\n\n# train the neural network\ndef train_network():\n\nsys.stdout.flush()\n\nnotes = get_notes()\n\n# get amount of pitch names\nn_vocab = len(set(notes))\n\nsys.stdout.write(\"\\nPreparing note sequences...\\n\")\nsys.stdout.flush()\n\nnetwork_input, network_output = prepare_sequences(notes, n_vocab)\n\nsys.stdout.write(\"\\nCreating CuDNNLSTM neural network model...\\n\")\nsys.stdout.flush()\n\nmodel = create_network(network_input, n_vocab)\n\nsys.stdout.write(\"\\nTraining CuDNNLSTM neural network model...\\n\\n\")\nsys.stdout.flush()\n\ntrain(model, network_input, network_output)\n\n# get all the notes and chords from the midi files\ndef get_notes():\n\n# remove existing data file if it exists\nif os.path.isfile(notesfile):\nos.remove(notesfile)\n\nnotes = []\n\nfor file in glob.glob(\"{}/*.mid\".format(mididirectory)):\nmidi = converter.parse(file)\n\nsys.stdout.write(\"Parsing %s ...\\n\" % file)\nsys.stdout.flush()\n\nnotes_to_parse = None\n\ntry: # file has instrument parts\ns2 = instrument.partitionByInstrument(midi)\nnotes_to_parse = s2.parts.recurse()\nexcept: # file has notes in a flat structure\nnotes_to_parse = midi.flat.notes\n\nfor element in notes_to_parse:\nif isinstance(element, note.Note):\nnotes.append(str(element.pitch))\nelif isinstance(element, chord.Chord):\nnotes.append('.'.join(str(n) for n in element.normalOrder))\n\nwith open(notesfile,'wb') as filepath:\npickle.dump(notes, filepath)\n\nreturn notes\n\n# prepare the sequences used by the neural network\ndef prepare_sequences(notes, n_vocab):\nsequence_length = 100\n\n# get all pitch names\npitchnames = sorted(set(item for item in notes))\n\n# create a dictionary to map pitches to integers\nnote_to_int = dict((note, number) for number, note in enumerate(pitchnames))\n\nnetwork_input = []\nnetwork_output = []\n\n# create input sequences and the corresponding outputs\nfor i in range(0, len(notes) - sequence_length, 1):\nsequence_in = notes[i:i + sequence_length] # needs to take into account if notes in midi file are less than required 100 ( mod ? )\nsequence_out = notes[i + sequence_length] # needs to take into account if notes in midi file are less than required 100 ( mod ? )\nnetwork_input.append([note_to_int[char] for char in sequence_in])\nnetwork_output.append(note_to_int[sequence_out])\n\nn_patterns = len(network_input)\n\n# reshape the input into a format compatible with CuDNNLSTM layers\nnetwork_input = numpy.reshape(network_input, (n_patterns, sequence_length, 1))\n# normalize input\nnetwork_input = network_input / float(n_vocab)\n\nnetwork_output = np_utils.to_categorical(network_output)\n\nreturn (network_input, network_output)\n\n# create the structure of the neural network\ndef create_network(network_input, n_vocab):\n\n'''\n\"\"\" create the structure of the neural network \"\"\"\nmodel = Sequential()\nmodel.compile(loss='categorical_crossentropy', optimizer='rmsprop',metrics=[\"accuracy\"])\n'''\n\nmodel = Sequential()\n\nreturn model\n\n# train the neural network\ndef train(model, network_input, network_output):\n\n# saver = CustomSaver()\n# history = model.fit(network_input, network_output, epochs=modelepochs, batch_size=50, callbacks=[tensorboard])\nhistory = model.fit(network_input, network_output, epochs=modelepochs, batch_size=50, callbacks=[CustomSaver()])\n\n# evaluate the model\nprint(\"\\nModel evaluation at the end of training\")\ntrain_acc = model.evaluate(network_input, network_output, verbose=0)\nprint(model.metrics_names)\nprint(train_acc)\n\n# save trained model\nmodel.save(modeldirectory + modelfileprefix + '_' + str(modelepochs) + '.model')\n\n# delete temp notes file\nos.remove(notesfile)\n\nif __name__ == '__main__':\ntrain_network()\n```\n```\n\nThis is the midi generation script “lstm_music_predict.py”\n\n``````\n# based on code from https://github.com/Skuldur/Classical-Piano-Composer\n# to use this script pass in;\n# 1. path to notes file\n# 2. path to model\n# 3. path to midi output\n# eg python -W ignore \"C:\\\\LSTM Composer\\\\lstm_music_predict.py\" \"C:\\\\LSTM Composer\\\\Bach.notes\" \"C:\\\\LSTM Composer\\\\Bach.model\" \"C:\\\\LSTM Composer\\\\Bach.mid\"\n\n# ignore all info and warning messages\nimport os\nos.environ['TF_CPP_MIN_LOG_LEVEL'] = '2'\nimport tensorflow as tf\ntf.compat.v1.logging.set_verbosity(tf.compat.v1.logging.ERROR)\n\nimport pickle\nimport numpy\nimport sys\nimport keras.models\n\nfrom music21 import instrument, note, stream, chord\nfrom keras.models import Sequential\nfrom keras.layers import Dense\nfrom keras.layers import Dropout\nfrom keras.layers import Activation\n\n# name of weights filename\nnotesfile = str(sys.argv)\nmodelfile = str(sys.argv)\nmidifile = str(sys.argv)\n\n# generates a piano midi file\ndef generate():\nsys.stdout.flush()\n\n#load the notes used to train the model\nwith open(notesfile, 'rb') as filepath:\n\nsys.stdout.write(\"Getting pitch names...\\n\\n\")\nsys.stdout.flush()\n\n# Get all pitch names\npitchnames = sorted(set(item for item in notes))\n# Get all pitch names\nn_vocab = len(set(notes))\n\nsys.stdout.write(\"Preparing sequences...\\n\\n\")\nsys.stdout.flush()\n\nnetwork_input, normalized_input = prepare_sequences(notes, pitchnames, n_vocab)\n\nsys.stdout.flush()\n\nmodel = create_network(normalized_input, n_vocab)\n\nsys.stdout.write(\"Generating note sequence...\\n\\n\")\nsys.stdout.flush()\n\nprediction_output = generate_notes(model, network_input, pitchnames, n_vocab)\n\nsys.stdout.write(\"\\nCreating MIDI file...\\n\\n\")\nsys.stdout.flush()\n\ncreate_midi(prediction_output)\n\n# prepare the sequences used by the neural network\ndef prepare_sequences(notes, pitchnames, n_vocab):\n# map between notes and integers and back\nnote_to_int = dict((note, number) for number, note in enumerate(pitchnames))\n\nsequence_length = 100\nnetwork_input = []\noutput = []\nfor i in range(0, len(notes) - sequence_length, 1):\nsequence_in = notes[i:i + sequence_length]\nsequence_out = notes[i + sequence_length]\nnetwork_input.append([note_to_int[char] for char in sequence_in])\noutput.append(note_to_int[sequence_out])\n\nn_patterns = len(network_input)\n\n# reshape the input into a format compatible with LSTM layers\nnormalized_input = numpy.reshape(network_input, (n_patterns, sequence_length, 1))\n# normalize input\nnormalized_input = normalized_input / float(n_vocab)\n\nreturn (network_input, normalized_input)\n\n# create the structure of the neural network\ndef create_network(network_input, n_vocab):\nreturn model\n\n# generate notes from the neural network based on a sequence of notes\ndef generate_notes(model, network_input, pitchnames, n_vocab):\n# pick a random sequence from the input as a starting point for the prediction\nstart = numpy.random.randint(0, len(network_input)-1)\n\nint_to_note = dict((number, note) for number, note in enumerate(pitchnames))\n\npattern = network_input[start]\nprediction_output = []\n\n# generate 500 notes\nfor note_index in range(500):\nprediction_input = numpy.reshape(pattern, (1, len(pattern), 1))\nprediction_input = prediction_input / float(n_vocab)\n\nprediction = model.predict(prediction_input, verbose=0)\n\nindex = numpy.argmax(prediction)\nresult = int_to_note[index]\nprediction_output.append(result)\n\npattern.append(index)\npattern = pattern[1:len(pattern)]\n\nif (note_index + 1) % 50 == 0:\nsys.stdout.write(\"{} out of 500 notes generated\\n\".format(note_index+1))\nsys.stdout.flush()\n\nreturn prediction_output\n\n# convert the output from the prediction to notes and create a midi file from the notes\ndef create_midi(prediction_output):\noffset = 0\noutput_notes = []\n\n# create note and chord objects based on the values generated by the model\nfor pattern in prediction_output:\n# pattern is a chord\nif ('.' in pattern) or pattern.isdigit():\nnotes_in_chord = pattern.split('.')\nnotes = []\nfor current_note in notes_in_chord:\nnew_note = note.Note(int(current_note))\nnew_note.storedInstrument = instrument.Piano()\nnotes.append(new_note)\nnew_chord = chord.Chord(notes)\nnew_chord.offset = offset\noutput_notes.append(new_chord)\n# pattern is a note\nelse:\nnew_note = note.Note(pattern)\nnew_note.offset = offset\nnew_note.storedInstrument = instrument.Piano()\noutput_notes.append(new_note)\n\n# increase offset each iteration so that notes do not stack\noffset += 0.5\n\nmidi_stream = stream.Stream(output_notes)\n\nmidi_stream.write('midi', fp=midifile)\n\nif __name__ == '__main__':\ngenerate()\n```\n```\n\nModel File Sizes\n\nOne downside to including neural networks with Visions of Chaos is file size. If model generation was quicker I would just include a button so the end user could train the model(s) themselves. But seeing as some of these training sessions can take days to train multiple models that is not really practical. A better solution is for me to do all the training and testing work and only include the best working models. This also means that the end user just has to click a button and the trained models are then used for the music compositions. I now download the 1 GB zip file of models automatically when the user starts the LSTM Composer mode for the first time.\n\nWhat’s Next?\n\nThe LSTM composer as shown in this post is the most basic usage of neural networks to compose music.\n\nI have found other neural network music composers that I will experiment with next so expect more music composition options to be included with Visions of Chaos in the future.\n\nJason.\n\n# Automatic Detection of Interesting Cellular Automata\n\nThis post has been in a draft state for at least a couple of years now. I revisit it whenever I get inspiration for a new idea. I wasn’t going to bother posting it until I had a better solution to the problem, but maybe these ideas can trigger a working solution in someone else’s mind.\n\nCompared to my other blog posts this one is more rambling as it follows the paths I have gone down so far when trying to solve this problem.\n\nObjective\n\nCellular automata tend to have huge parameter search spaces to find interesting results within. The vast majority of rules within this space will be junk rules with only a small fraction of a percentage being interesting rules. I have spent way too many hours repeatedly trying random rules when looking for new interesting cellular automata. Between the boring rules that either die out or rules that go chaotic there is that sweet spot of interesting rules. Finding these interesting rules is the problem.", null, "My ideal goal has always been to be able to run random rules repeatedly hands free and have software that is “clever” enough to determine the difference of interesting vs boring results. If the algorithms are good enough at detecting interesting then you can come back to the computer hours or days later and have a set of rules in a folder with preview images and/or movies to check out.\n\nI want the smarts to be smart enough to work with a variety of CA types beyond the basic 2 state 2D cellular automata. Visions of Chaos contains many varieties of cellular automata with varying maximum cell states, dimensions and neighborhoods that I ultimately would like to be able to click a “Look for interesting rules” button.\n\nInteresting Defined\n\nInteresting is a very loose term. Maybe a few examples will help define what I mean when I say interesting.\n\nBoring results are when a CA stabilizes to a fixed pattern or a pattern with very minimal change between steps.", null, "", null, "", null, "Chaotic results are when the CA turns into a screen of static with no real discernible patterns or features like gliders or other CA related structures. For a CA classifier these rules are also boring.", null, "", null, "", null, "Interesting is anything else. Rules like Game of Life, Brian’s Brain and others that create evolvable structures that survive after multiple cycles of the CA. This is what I want the software to be able to detect.", null, "Conway’s Game of Life – 23/3/2\nBrian’s Brain – /2/3\nFireballs – 346/2/4\n\nMy Previous Search Methods\n\n1. Random rules. Repeatedly generate random rules hoping to see an interesting result. Tedious to say the least, although the majority of the interesting cellular automata rules I have found over the years have been through repeatedly trying different random rules. While a boring TV show or movie is on I can repeatedly hit F3, F4 and Enter in Visions of Chaos while looking for interesting results. F3 stops the current CA running, F4 shows the settings dialog, Enter clicks the Random Rule button.\n\n2. Brute force all possible rules. Only applicable for when the total number of rules is small (possible for some of the simpler 1D CAs). Most 2D CAs have millions or billions of possible rules and brute force rendering them all and then checking manually is impossible.\n\n3. Mutating existing interesting rules. If you get an interesting rule, you can try mutating the rule slightly to try alternatives that may behave similarly yet better to the rule. Slightly usually means toggling one of the survival/birth checkboxes on/off. This has occasionally helped me find interesting rules or refine a rule to that sweet spot. The problem with CAs is that even changing one checkbox will usually result in a completely different result. The good results do not tend to “clump” together in the parameter space.\n\nThe rest of this blog post contains methods others and myself have tried to classify cellular automata behavior.\n\nWolfram Classification", null, "Stephen Wolfram defined a rough set of 4 classifications for CAs.\n\nClass 1: Nearly all initial patterns evolve quickly into a stable, homogeneous state. Any randomness in the initial pattern disappears.\n\nClass 2: Nearly all initial patterns evolve quickly into stable or oscillating structures. Some of the randomness in the initial pattern may filter out, but some remains. Local changes to the initial pattern tend to remain local.\n\nClass 3: Nearly all initial patterns evolve in a pseudo-random or chaotic manner. Any stable structures that appear are quickly destroyed by the surrounding noise. Local changes to the initial pattern tend to spread indefinitely.\n\nClass 4: Nearly all initial patterns evolve into structures that interact in complex and interesting ways, with the formation of local structures that are able to survive for long periods of time.\n\nClasses 1 to 3 would be considered “boring” for anyone trying random rules. Class 4 is that “sweet spot” of CAs that something interesting happens between dying out and chaotic explosions.\n\nYou can look at a CA after it has been discovered and put it into one of those 4 categories but that doesn’t help detecting interesting rules in Class 4.\n\nOther Methods From Various Papers\n\nHere are some other classification methods in papers I found or saw mentioned elsewhere. The mathematics is beyond me for most of them. I wish papers included a small snippet of source code with them that shows the math. I always find it much easier understanding and implementing some source code rather than try and understand formal equations.\n\nBehavioral Metrics\n\nEntropy\n\nWolfram’s Universality And Complexity In Cellular Automata discusses “entropy” values that I don’t understand.\n\nLyapunov Exponents\n\nKolmogorov–Chaitin Complexity\n\nGenetic Algorithms\n\nOther Papers\n\nMergeLife\n\nJeff Heaton uses genetic mutations to evolve cellular automata.\n\nLangton’s Lambda", null, "Chris Langton defined a single number that can help predict if a CA will fall within the ordered realm. See his paper Computation at the edge of chaos for the mathematical definitions etc.\n\nLangton called this number lambda. According to this page Lambda is calculated by counting the number of cells that have just been “born” that step of the CA and dividing it by the total CA cells. This gives a value between 0 and 1.\n\nL = newlyborn/totalcellcount\nL within 0.01 and 0.15 means a good rule to further investigate.\n\nSo if the grid is 20×20 in size and there were 50 cells that were newly born that CA cycle, then lambda would be 50/20×20=0.125\n\nI skip the first 100 CA cycles to allow the CA to settle down and then average the lambda value for the next 50 steps.\n\nAs stated here there is no single value of lambda that will always give an interesting result. Langton’s paper and example applet are only concerned with 1D CA examples. I really want to find methods to search and classify 2D, 3D (and even 4D) cellular automata.\n\nRampe’s Lambdas\n\nFor lack of a better name, these are the “Rampe’s Lambda” values I experimented with as alternatives to Langton’s Lambda.\n\nR1 within 0.9 and 1.1 means a good rule to further investigate.\n\nR2 within 0.001 and 0.005 means a good rule to further investigate.\n\nR3 within 0.01 and 0.8 means a good rule to further investigate.\n\nR4 within 0.01 and 0.23 means a good rule to further investigate.\n\nR5 = % change in Langton’s Lambda between the last and current CA cycle\nR5 within 0.01 and 0.1 means a good rule to further investigate.\n\nAgain, skip the first 100 cycles of the CA and then use the average lambda from the following 50 cycles.\n\nLambda Results\n\nAll of them (both Langton and my “Rampe” variations) are next to useless from my tests. I ran a bunch of known good rules and got mixed results. All the lambda’s gave enough false positives to not be of any use in searching for interesting new rules. You may as well use a random number generator to classify the rules.\n\nMaybe they can be used to weed out the extreme class 1, 2 and 3 uninteresting dead rules, but they are not useful for classifying if a class 4 like result is interesting or not.\n\nFractal Dimension", null, "Another method I tried is finding the fractal dimension of the CA image using box counting. Fractal dimensions are unlike the usual 1D, 2D and 3D fixed dimensions and for a 2D image are and floating point value between 0 and 2.\n\nThe above screenshot shows the fractal dimension tests on existing sample interesting CA files. The results are all over the place with no “sweet spot” of dimension correlating to interesting. The way it works is that each CA is run for 50 steps, the image is converted to black and white (non black pixels in the image are changed to white) and then the dimension is calculated using the box counting method.\n\nIncreasing the range of dimension for “good” detection may result in the known interesting rules to pass the tests, but it then thinks a lot of uninteresting rules are then interesting, meaning you still need to manually sort good vs bad.\n\nA fractal dimension between 1.0 and 1.4-1.5 can help weed out obvious “bad” results, but is really not helpful in hands free searching.\n\nCompression Based Searching\n\nAnother new interesting idea on CA searching comes from Hugo Cisneros, Josef Sivic and Tomas Mikolov. Using data compression algorithms to rate CAs.", null, "Their paper “Evolving Structures in Complex Systems” available here is an interesting read.\n\nSource code accompanying the paper is provided here.\n\nNeural Networks – Part 1\n\nThis was an idea I had for a while. Train a neural network to detect if a CA rule is interesting or not.\n\nI was able to implement a rudimentary neural network system after watching these excellent videos from Dan Shiffman.\n\nI went from almost zero knowledge of the internals of neural networks to much more comfortable and being able to code a working NN system. If you want to learn about the basics of coding a neural network I highly recommend Dan’s playlist.\n\nFor a neural network to be able to give you meaningful output (in this case if a CA rule is interesting or not) it needs to be trained with known good and bad data.\n\nI tried creating a neural network with 19 inputs (9 for survival states, 9 for birth states and 1 for number of states) to cover the possible CA settings, ie", null, "The neural network has 19 inputs, a number of neurons in the hidden layer and a single output neuron that does the interestingness prediction.", null, "I mainly kept the hidden neuron count the same as the inputs, but I did experiment with other counts as the next diagram shows.", null, "The known good and bad rules are fed through the neural network in random order for 10 million or more times. You can see how well the network is “learning” by tracking the mean squared error. As you repeatedly feed the network known data the error value should drop meaning the network is becoming more accurate at predicting the results you train it with.\n\nOnce the network is trained, you can run random rules and see if the prediction of the network matches your rating of if the CA is interesting or not. You can also repeatedly try random rules until they pass a threshold level of interesting. Every time a prediction is made the human can rate if the detection was correct. These human ratings are added back to the good and bad rule training pool so they can be used the next time the network is trained.\n\nThe end result is “just OK”. I used a well trained network (with a mean squared error of around 0.001) and got it to repeatedly try random rules until it found a rule it predicted would be interesting. The results are not always interesting. More interesting than purely sitting there clicking random repeatedly as I have done in the past, but there are still a lot of not interesting rules spat out. If I let the network run for a few hours and got it to save every rule it predicted to be interesting I would still have a tedious process of weeding out the actual interesting rules.\n\nI don’t think inputs from survival and birth rules is the best way of doing this. This is because a toggle of a single survival or birth checkbox will usually drastically change the results from interesting to boring or just chaos. Also changing the maximum states each cell can have by 1 will cause well behaved rules to change into chaotic mess results.\n\nOne idea I need to try is using a basic NN like this that uses the lambda values above for inputs. Maybe then it can work out which combination of lambdas (and maybe fractal dimension) work together to create good rules. This is worth experimenting with when I get some time.\n\nNeural Networks – Part 2\n\nThis time I am trying to get the network to detect interesting CAs by using images from a frame of the CAs. For each of the known good and bad rules I take the 100th frame as an input. I also repeat each of the rules 100 times to get 100 samples of each rule.\n\nIf I use a 64×64 sized grayscale image then there will now be 4,096 inputs to the network. Add another 100 hidden nodes and that makes a large and much slower network when training.\n\nRun the CA rules on a 64×64 sized grid, convert the image pixels into the 4,096 inputs and train the network.\n\nSo far, no good results. The mean squared error falls very slowly. Maybe it would get better after days of training, but I am not that patient yet.\n\nThis online example and this article show how this method (a fully connected neural network) is never as accurate as a convolutional neural network. So, onto Part 3…\n\nNeural Networks – Part 3\n\nMy next idea was to try using Convolutional Neural Networks. See here for a nice explanation of convolutional neural networks.", null, "CNN’s are made for image processing, feature extraction and detection. If a CNN can be trained to recognize digits and tell if a photo is of a cat or a dog then I should be able to use a CNN to “look at” a frame of a cellular automaton and tell me if it is interesting or not.\n\nAfter watching a bunch of YouTube university lectures and tutorials on CNNs I decided not to extend my existing neural network code to handle CNNs. For the network sizes I will be training I need a real world library. I chose Google’s TensorFlow.", null, "TensorFlow supports GPU acceleration with CUDA and is magnitudes faster and more reliable than anything I could code.\n\nOnce I managed to get Python, TensorFlow, Keras, CUDA and cuDNN installed correctly I was able to execute Python scripts from within Visions of Chaos and successfully run the example TensorFlow CNN MNIST code. That showed I had all the various components working as expected.\n\nCreating Training Data for the CNN\n\nAcquiring clean and accurate training data is vital for a good model. The more data the better.\n\nI used the following steps to create a lot of training images;\n\n1. Take a bunch of CA rules that I had previously ranked as either good or bad.\n\n2. Run all of them over a 128×128 sized grid for 100 steps and save the 100th frame as a grayscale jpg file.\n\n3. Step 2 can be repeated multiple times to increase the amount of training data. CAs starting from a random grid will always give you a unique 100th frame so this is an easy way to generate lots more training data.\n\n4. Copy some of the generated images into a test folder. I usually move 1/10th of the total generated images into a test folder. These will be used to evaluate how accurate the model is at predictions once it has been trained. You want test data that is different to the data used to train and validate the model.", null, "Examples of good CA frames\n\nQuantity and Dimensions of Training Data Images\n\nI tried image sizes between 32×32 pixels and 128×128 pixels. I also tried various zoomed in CA images with each cell being 2×2 pixels rather than a single pixel per cell.\n\nFor image counts I tried between 10,000 up to 300,000.\n\nAfter days of generating images and training and testing models I found a good balance between image size and model accuracy was images 128×128 pixels in size with a single pixel per CA cell (so a CA grid of 128×128 too).\n\nI also experimented with blurring the images thinking that may help search for more general patterns, but it did not seem to make any difference in the number found or accuracy of results.\n\nOne thing working with neural networks teaches you is patience. Generating the images is the slowest part of these experiments. If anyone is willing to gift me some decent high end CPUs and GPUs I would put them to good use.\n\nCustom Input for CNNs\n\nThe best videos I found on using CNNs with custom images were these videos on YouTube by sentdex. Parts 1 to 6 of that playlist got me up and running.\n\nCreating the Training Data for TensorFlow\n\nOnce you have your training images they need to be converted into a data format that TensorFlow can be trained with.\n\nAgain, I recommend the following sentdex video that covers how to create the training data.\n\nThe process to convert the training images into training data is fast and should not take longer than a minute or two.\n\nModel Variations\n\nTime to actually use this training data to train a convolutional neural network (what TensorFlow calls a model).\n\nThere are a wide variety of model and layer types to experiment with. For CNNs you basically start with one or more Conv2D layers followed by one or more Dense layers and finally a single output node to predict a probability of the image being good or bad.\n\nHere are some models I tried during testing. From various sources and videos and pages I have seen. Running on an Nvidia 1080 GPU took around 2 hours per model to train (50 epochs each with 100,000 training images), which seemed lightning fast after waiting 30 hours for my training images to generate.\n\n```\n`# Version 1`\n`# Original model from sentdex videos`\n`# https://youtu.be/WvoLTXIjBYU`\n\n`model = Sequential()`\n\n`model.add(Conv2D(64, (3,3), input_shape = X.shape[1:]))`\n`model.add(Activation(\"relu\"))`\n`model.add(MaxPooling2D(pool_size=(2,2)))`\n\n`model.add(Conv2D(64, (3,3)))`\n`model.add(Activation(\"relu\"))`\n`model.add(MaxPooling2D(pool_size=(2,2)))`\n\n`model.add(Flatten())`\n\n`model.add(Dense(64))`\n`model.add(Activation(\"relu\"))`\n\n`model.add(Dense(1))`\n`model.add(Activation(\"sigmoid\"))`\n\n`model.compile(loss=\"binary_crossentropy\",optimizer=\"adam\",metrics=[\"accuracy\"])`\n`model.fit(X, y, batch_size=50, epochs=50, validation_split=0.3)````\n\nWhen the 50 epochs finish, you can plot the accuracy and loss vs the validation accuracy and loss.", null, "Version 1 gave these results;\ntest loss, test acc: [0.13674676911142003, 0.9789666691422463]\n98% accuracy with a loss of 13%\nWhen I test a different unique set of images as test data I get;\n14500 good images predicted as good – 301 good images predicted as bad – 97.97% predicted correctly\n14653 bad images predicted as bad – 184 bad images predicted as good – 98.76% predicted correctly\n\nOne thing the above “Model loss” graph shows is overfitting. The val_loss graph should follow the loss graph and continue to go down. Instead of going down the line starts going up around the 5th epoch. This is an obvious sign of overfitting. Overfitting is bad. We don’t want overfitting. See here for more info on overfitting and how to avoid it.\n\nThe second suggestion from here mentions dropouts. Dropouts remove random links between nodes in the model network as it trains. This can help reduce overfitting. So let’s give that a go.\n\n```\n`# Version 2`\n`# Original model from sentdex videos`\n`# https://youtu.be/WvoLTXIjBYU`\n`# Adding dropouts to stop overfitting`\n\n`model = Sequential()`\n\n`model.add(Conv2D(64, (3,3), input_shape = X.shape[1:]))`\n`model.add(Activation(\"relu\"))`\n`model.add(MaxPooling2D(pool_size=(2,2)))`\n`model.add(Dropout(0.4))`\n\n`model.add(Conv2D(64, (3,3)))`\n`model.add(Activation(\"relu\"))`\n`model.add(MaxPooling2D(pool_size=(2,2)))`\n`model.add(Dropout(0.4))`\n\n`model.add(Flatten())`\n\n`model.add(Dense(64))`\n`model.add(Activation(\"relu\"))`\n`model.add(Dropout(0.4))`\n\n`model.add(Dense(1))`\n`model.add(Activation(\"sigmoid\"))`\n\n`model.compile(loss=\"binary_crossentropy\",optimizer=\"adam\",metrics=[\"accuracy\"])`\n`model.fit(X, y, batch_size=50, epochs=50, validation_split=0.3)````\n\n50 epochs finished with this graph.", null, "Now the validation loss continues to generally go down with the loss graph. This shows overfitting is no longer occurring.\n\nVersion 2 gave these results;\ntest loss, test acc: [0.037338864829847204, 0.9866000044345856]\n98% accuracy with a 13% loss\nWhen I test a different unique set of images as test data I get;\n14151 good images predicted as good – 68 good images predicted as bad – 99.52% predicted correctly\n14326 bad images predicted as bad – 12 bad images predicted as good – 99.92% predicted correctly\n\n```\n`# Version 3`\n`# https://towardsdatascience.com/applied-deep-learning-part-4-convolutional-neural-networks-584bc134c1e2`\n\n`model = Sequential()`\n\n`model.add(Conv2D(32, (3,3), input_shape = X.shape[1:]))`\n`model.add(Activation(\"relu\"))`\n`model.add(MaxPooling2D(pool_size=(2,2)))`\n\n`model.add(Conv2D(64, (3,3)))`\n`model.add(Activation(\"relu\"))`\n`model.add(MaxPooling2D(pool_size=(2,2)))`\n\n`model.add(Conv2D(128, (3,3)))`\n`model.add(Activation(\"relu\"))`\n`model.add(MaxPooling2D(pool_size=(2,2)))`\n\n`model.add(Conv2D(128, (3,3)))`\n`model.add(Activation(\"relu\"))`\n`model.add(MaxPooling2D(pool_size=(2,2)))`\n\n`model.add(Flatten())`\n`model.add(Dropout(0.5))`\n\n`model.add(Dense(512))`\n`model.add(Activation(\"relu\"))`\n\n`model.add(Dense(1))`\n`model.add(Activation(\"sigmoid\"))`\n\n`model.compile(loss=\"binary_crossentropy\",optimizer=\"adam\",metrics=[\"accuracy\"])`\n`model.fit(X, y, batch_size=50, epochs=50, validation_split=0.3)````\n\nGraphs looked good without any obvious overfitting.\n\nVersion 3 gave these results;\ntest loss, test acc: [0.03628389219510306, 0.9891333370407422]\n98% accuracy with 3% loss. Getting better.\nWhen I test a different unique set of images as test data I get;\n14669 good images predicted as good – 59 good images predicted as bad – 99.60% predicted correctly\n14490 bad images predicted as bad – 62 bad images predicted as good – 99.57% predicted correctly\n\n```\n`# Version 4`\n`# http://www.dsimb.inserm.fr/~ghouzam/personal_projects/Simpson_character_recognition.html`\n\n`model = Sequential()`\n\n`model.add(Conv2D(32, (3,3), input_shape = X.shape[1:]))`\n`model.add(Conv2D(32, (3,3)))`\n`model.add(Activation(\"relu\"))`\n`# BatchNormalization better than Dropout? https://www.kdnuggets.com/2018/09/dropout-convolutional-networks.html`\n`# model.add(BatchNormalization())`\n`model.add(MaxPooling2D(pool_size=(2,2)))`\n`model.add(Dropout(0.25))`\n\n`model.add(Conv2D(64, (3,3)))`\n`model.add(Conv2D(64, (3,3)))`\n`model.add(Activation(\"relu\"))`\n`# BatchNormalization better than Dropout? https://www.kdnuggets.com/2018/09/dropout-convolutional-networks.html`\n`# model.add(BatchNormalization())`\n`model.add(MaxPooling2D(pool_size=(2,2)))`\n`model.add(Dropout(0.25))`\n\n`model.add(Conv2D(128, (3,3)))`\n`model.add(Conv2D(128, (3,3)))`\n`model.add(Activation(\"relu\"))`\n`# BatchNormalization better than Dropout? https://www.kdnuggets.com/2018/09/dropout-convolutional-networks.html`\n`# model.add(BatchNormalization())`\n`model.add(MaxPooling2D(pool_size=(2,2)))`\n`model.add(Dropout(0.5))`\n\n`model.add(Flatten())`\n\n`model.add(Dense(64))`\n`model.add(BatchNormalization())`\n`model.add(Activation(\"relu\"))`\n\n`model.add(Dense(32))`\n`model.add(BatchNormalization())`\n`model.add(Activation(\"relu\"))`\n\n`model.add(Dense(16))`\n`model.add(BatchNormalization())`\n`model.add(Activation(\"relu\"))`\n\n`model.add(Dense(1))`\n`model.add(Activation(\"sigmoid\"))`\n\n`model.compile(loss=\"binary_crossentropy\",optimizer=\"adam\",metrics=[\"accuracy\"])`\n`model.fit(X, y, batch_size=50, epochs=50, validation_split=0.3)````\n\nFor this model I threw in multiple ideas from all previous models and more.\n\nVersion 4 gave these results;\ntest loss, test acc: [0.031484683321298994, 0.9896000043551128]\n99% accuracy with a 3% loss. Best result so far.\nWhen I test a different unique set of images as test data I get;\n14383 good images predicted as good – 119 good images predicted as bad – 99.18% predicted correctly\n14845 bad images predicted as bad – 4 bad images predicted as good – 99.97% predicted correctly\n\nFor the rest of my tests I used Version 4 for all training.\n\nSee the sentdex videos above for a good example of how to tweak models and see how the variations rate. Use TensorBoard to see how they compare and optimize them.", null, "TensorBoard has other interesting histograms it will generate from your training like the following. I have no idea what this is telling me yet, but they look cool. Using histograms did seem to slow down the training with extended pauses between epochs, so unless you need them I recommend disabling them.", null, "Testing the Trained Model\n\nNow it is finally time to put the model to the test.\n\nRandomly set a CA rule, run it for 100 generations and then use model.predict on the 100th frame. This takes around 6 seconds per random rule.\n\nThe model.predict function returns a floating point value between 0 and 1.\nBetween 0 and 0.2 are classified as bad.\n0.2 to 0.95 are classified as unsure.\n0.95 to 1 are classified as good.\n\nThe prediction accuracy is better than any of the other methods shown previously in this post.\n\nThe rules it did detect in the bad category were all bad, so it does a great job there. No interesting rules got incorrectly classified as bad from my tests. I can safely ignore rules classified as bad which speeds up the search time as I don’t have to re-run the rules and create a sample movie.\n\nThe detected good rules did have a blend of interesting and boring/chaotic, but there were a lot less of them to check. Roughly 1% of total random rules are classified as good. The rules the model incorrectly predicts as interesting can be moved into the “known bad” folder and can be added to the next trained model (another 40 hours or so of my PC churning away generating images and training a new model).\n\nThe rules it predicted in the unsure 0.2 to 0.95 range did have features that were in the range between good and bad. Some of them would have made excellent good samples if only they were not as chaotic and “busy”.\n\nResults\n\nHere are some examples found from overnight convolutional neural network searches.", null, "TF247445 – 4567/2358/5 – Brian’s Brain with islands", null, "TF394435 – 34/256/3 – Another Brian like rule", null, "TF263299 – 3/25/3 – Over excited brain rule", null, "TF174642 – 15678/12678/2 – Solid islands grow amongst static", null, "TF1959733 – 1235678/23478/5 – Solidification", null, "TF2254533 – 0478/2356/5 – Waves with stable pixels\n\nOther CNN Problems and Ideas\n\nOne problem is that CNNs seem to only detect shapes/gliders/patterns that are similar to the training data. After days of testing self searching with the CNN models there were no brand new different rules discovered. Just a bunch of very similar to existing rules and maybe a few slight tweaks. For example if a CNN is trained using only examples of Conway’s Game of Life CA then it is not going to predict Brian’s Brain is interesting if it randomly tries the rule for Brian’s Brain. The CNN needs to have previously seen the rule(s) it will detect as interesting. I did see slight variations found and scored as interesting, but for a new CA type without a lot of “good” rules to train on the CNN is not going to have problems finding new/different interesting rules. The main reason I want a “search for interesting” function is for when I have a new type of CA without a lot of known good rules. I want the search to be able to work without needing hundreds or thousands of examples of already rated good vs bad. Otherwise I need to sit there trying random rules for hours and manually rate them good or bad before training a new model specific to that CA rule.\n\nMaybe using single frames is not the best idea. Maybe the difference between the 99th and 100th frame? Maybe a blur or average of 3 frames? This is still to be experimented with when I have another week to spend generating images and training and testing new models.\n\nThen I thought maybe I am over training the models. If you train a neural network for too long it will overfit and then only be able to recognize the data you trained it with. This is as if it memorizes only the good data you gave it as good. It cannot generalize to detect other different good results as good. This results in new interesting CAs being potentially classified as bad. I did try lowering the training epochs from 50 to 10 to see if that helped detect more generalized interesting CA rules but it didn’t seem to make any difference. Even lowering it to 5 epochs trained a model that was still accurate at predictions. Plus the difference between random frames of good CAs shows it can detect gliders at different locations within frames.\n\nRather than train a model for each type of CA, train a model with examples from multiple CA types. Try and make the model more capable of general CA detection. Maybe it could then detect newer shapes/gliders in different new CA rules if it has a good general idea of what interesting CA features are from multiple different CAs. This may work? Another one for the to do list.\n\nConvolutional Neural Networks (and neural networks in general) are not an instant win solution. You do need to do a lot of research about the various settings and do a lot of testing to get a good model which you can then use to predict the “things” you want the model to predict. But once you get a well trained model CNNs can be almost magical in how they can learn and be useful when solving problems.\n\nThe more I experiment with and learn about neural networks only makes me want to continue the journey. They really are fascinating. Using TensorFlow and Keras are a great way to get into the world of neural networks without having to code your own neural network system from scratch. I do recommend at least coding a basic feed forward neural network to get a good grip on the basics. When you jump into Keras the terminology will make more sense. YouTube has lots of good neural network related videos.\n\nAvailability to End Users\n\nI have now included the trained (20 epochs Version 4 to hopefully leave a little room for finding more unique results) TensorFlow CNN model with Visions of Chaos. That means the end user does not need to do any image generation or training before using the CNN for searching. Python and TensorFlow need to be installed first, but after that the user can start a hands free search for interesting rules. When TensorFlow is installed and detected a search button appears on the 2D Cellular Automata dialog. Clicking Search starts a hands free random search and classification.", null, "The other search methods above are still hidden as they do not predict interesting with a high enough accuracy.\n\nThe End (for now)\n\nIf you managed to get this far, thanks for reading." ]

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[ "# Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.\n\n### Popular Tutorials in Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.\n\n• #### How Do You Find Values for Variables in the Angles of a Quadrilateral To Make it a Parallelogram?\n\nWhen you're given a quadrilateral with some of the interior angles defined with variables, you can find what values those variables need to have to make that quadrilateral a parallelogram. Follow along with this tutorial to learn what steps to take to get the answer!\n\n• #### How Do You Use the Diagonals of a Rectangle to Find the Value of a Variable?\n\nWhen you make diagonals inside a rectangle, those diagonals are congruent. With this information, you can find the value of a variable that's part of a measurement of a diagonal. This tutorial shows you the steps.\n\n• #### How Do You Find the Value for a Variable in the Angles of a Quadrilateral To Make it a Rhombus?\n\nA parallelogram needs to have certain qualities in order to be a rhombus. In this tutorial, you'll use your knowledge of these shapes in order to find the value for a variable that will make a given parallelogram a rhombus.\n\n• #### What is a Parallelogram?\n\nA parallelogram is a special type of quadrilateral with some special properties. In this tutorial, take a look at parallelograms and learn what kinds of quadrilaterals can also be called parallelograms!" ]

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[ "### 3. The Interior Structure of a Star\n\nNotice that in the {7/3} star,", null, "we see a {7/2} star inscribed in the circle. The {7/2} star is in the orientation which is commonly used by law enforcement agencies.\n\nThis illustrates the following result.\n\nTheorem 3.1: (Coxeter ) If 1 < k < n/2, then inside an {n/k} star is an {n/k-1} star.\n\nTheorem 3.2: (Coxeter ) If 1 < k < n/2, then for all 1 < j < k there will be an {n/j} star inside {n/k}.\n\nExample: In this example we look at the stars inside the {15,7} star.\n\nWhile there are no other indiscrete stars inside an n-gon each {n/j} star where j is between 1 and k has an n-gon inside of it, so the n-gons play a role of central importance in this theory. If the discrete star and the asterisk are corresponding degenerate cases at opposite ends of the spectrum, then the star which corresponds to the n-gon at the opposite end of the spectrum would be the {n/[(n-1)/2]} star in that the n-gon is contained in every indiscrete n pointed star except for the asterisk, and the {n/[(n-1)/2]} star contains every n pointed star except for the asterisk.\n\nRemark: If n is prime, then all n pointed stars are simple. But if n is not prime then one will generally find composite stars inside simple stars and simple stars inside composite stars.\n\nNoticing that stars are made up of concentric rings of points will make it easier for us to analyze their structure.\n\nTheorem 3.3: If 1 < k < n/2, then, in the {n/k} star, the lines intersect at nk points.\n\nAfter determining how many points there are in the figures, it seems reasonable to ask how many regions there are and what types of figures these regions would be.\n\nTheorem 3.4: If 1 < k < n/2, then in an {n/k} star there are 1 + nk - n regions. They consist of\n\n1 regular convex n-gon, and\n\nif k > 1, there will be n triangles, and" ]

[ null, "http://web.sonoma.edu/users/w/wilsonst/papers/stars/illos/s7-3.gif", null ]

[ "With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.\n\nNo credit card required\n\nIndex\n\nA\n\nAbel, Niels Henrik\n\nAbsolute value:\n\nof a complex number\n\nas distance on the number line\n\nequations involving\n\nfunction\n\nof a function\n\ninequalities\n\nproperties of\n\nof a real number\n\nAcceleration due to gravity:\n\non the Earth\n\nof the Moon\n\nAcute angle\n\ndefinition of\n\ndomain of\n\nAddition rule of probability\n\nAddition of two vectors\n\nAgnesi, Maria\n\nAlgebra, Fundamental Theorem of\n\nAlgebraic expression\n\nAlgebraic function\n\nAmbient temperature\n\nAmbiguous case (Law of Sines)\n\nAmplitude:\n\nof cosine graphs\n\ndefinition of\n\nof sine graphs\n\nAngle between two vectors\n\nAngle(s):\n\nacute\n\ncentral\n\ncomplementary\n\ncoterminal\n\ndefinition of\n\ndegree measure of\n\nof depression\n\nof elevation\n\ninitial side of\n\nobtuse" ]

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[ "# Matplotlib显示灰度图¶\n\n## 概要¶\n\nkeywords Matplotlib Grayscale cvtColor\n\n## 转变为灰度图并显示¶\n\n# -*- coding: utf-8 -*-\nimport numpy as np\nimport cv2\n# 引入Python的可视化工具包 matplotlib\nfrom matplotlib import pyplot as plt\n\n# 导入一张图像 模式为彩色图片\n\n# 将色彩空间转变为灰度图并展示\ngray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)\n\nplt.imshow(gray)\n\n# 隐藏坐标系\nplt.axis('off')\n# 展示图片\nplt.show()", null, "def print_img_info(img):\nprint(\"================打印一下图像的属性================\")\nprint(\"图像对象的类型 {}\".format(type(img)))\nprint(img.shape)\nprint(\"图像宽度: {} pixels\".format(img.shape))\nprint(\"图像高度: {} pixels\".format(img.shape))\n# GRAYScale 没有第三个维度哦， 所以这样会报错\n# print(\"通道: {}\".format(img.shape))\nprint(\"图像分辨率: {}\".format(img.size))\nprint(\"数据类型: {}\".format(img.dtype))\n\nprint_img_info(gray)\n\n\n图像对象的类型 <class 'numpy.ndarray'>\n(182, 277)\n\n\n\nprint(\"打印图片局部\")\nprint(gray[100:105, 100:105])\n\n\nroi图片像素点格式如下。\n\n打印图片局部\n[[221 221 221 221 219]\n[220 220 220 220 219]\n[219 219 219 219 218]\n[219 219 219 219 218]\n[214 215 215 216 216]]\n\n\n## 给matplotlib添加cmap显示灰度图¶", null, "", null, "# 需要添加colormap 颜色映射函数为gray\nplt.imshow(gray, cmap=\"gray\")\n\n\nImageDisplayByMatplotlib_Grayscale.py\n\n# -*- coding: utf-8 -*-\nimport numpy as np\nimport cv2\n# 引入Python的可视化工具包 matplotlib\nfrom matplotlib import pyplot as plt\n\ndef print_img_info(img):\nprint(\"================打印一下图像的属性================\")\nprint(\"图像对象的类型 {}\".format(type(img)))\nprint(img.shape)\nprint(\"图像宽度: {} pixels\".format(img.shape))\nprint(\"图像高度: {} pixels\".format(img.shape))\n# GRAYScale 没有第三个维度哦， 所以这样会报错\n# print(\"通道: {}\".format(img.shape))\nprint(\"图像分辨率: {}\".format(img.size))\nprint(\"数据类型: {}\".format(img.dtype))\n\n# 导入一张图像 模式为彩色图片\n\n# 将色彩空间转变为灰度图并展示\ngray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)\n\n# 打印图片信息\n# print_img_info(gray)\n\n# 打印图片的局部\n# print(\"打印图片局部\")\n# print(gray[100:105, 100:105])\n\n# plt.imshow(gray)\n# 需要添加colormap 颜色映射函数为gray\nplt.imshow(gray, cmap=\"gray\")\n\n# 隐藏坐标系\nplt.axis('off')\n# 展示图片\n\nplt.show()\n# 你也可以保存图片， 填入图片路径就好\n# plt.savefig(\"cat_gray_01.png\")", null, "", null, "" ]

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[ "# #013d71 Color Information\n\nIn a RGB color space, hex #013d71 is composed of 0.4% red, 23.9% green and 44.3% blue. Whereas in a CMYK color space, it is composed of 99.1% cyan, 46% magenta, 0% yellow and 55.7% black. It has a hue angle of 207.9 degrees, a saturation of 98.2% and a lightness of 22.4%. #013d71 color hex could be obtained by blending #027ae2 with #000000. Closest websafe color is: #003366.\n\n• R 0\n• G 24\n• B 44\nRGB color chart\n• C 99\n• M 46\n• Y 0\n• K 56\nCMYK color chart\n\n#013d71 color description : Very dark blue.\n\n# #013d71 Color Conversion\n\nThe hexadecimal color #013d71 has RGB values of R:1, G:61, B:113 and CMYK values of C:0.99, M:0.46, Y:0, K:0.56. Its decimal value is 81265.\n\nHex triplet RGB Decimal 013d71 `#013d71` 1, 61, 113 `rgb(1,61,113)` 0.4, 23.9, 44.3 `rgb(0.4%,23.9%,44.3%)` 99, 46, 0, 56 207.9°, 98.2, 22.4 `hsl(207.9,98.2%,22.4%)` 207.9°, 99.1, 44.3 003366 `#003366`\nCIE-LAB 25.369, 4.702, -34.765 4.661, 4.536, 16.252 0.183, 0.178, 4.536 25.369, 35.081, 277.702 25.369, -14.618, -43.607 21.297, 1.797, -30.335 00000001, 00111101, 01110001\n\n# Color Schemes with #013d71\n\n• #013d71\n``#013d71` `rgb(1,61,113)``\n• #713501\n``#713501` `rgb(113,53,1)``\nComplementary Color\n• #01716d\n``#01716d` `rgb(1,113,109)``\n• #013d71\n``#013d71` `rgb(1,61,113)``\n• #010571\n``#010571` `rgb(1,5,113)``\nAnalogous Color\n• #716d01\n``#716d01` `rgb(113,109,1)``\n• #013d71\n``#013d71` `rgb(1,61,113)``\n• #710105\n``#710105` `rgb(113,1,5)``\nSplit Complementary Color\n• #3d7101\n``#3d7101` `rgb(61,113,1)``\n• #013d71\n``#013d71` `rgb(1,61,113)``\n• #71013d\n``#71013d` `rgb(113,1,61)``\n• #017135\n``#017135` `rgb(1,113,53)``\n• #013d71\n``#013d71` `rgb(1,61,113)``\n• #71013d\n``#71013d` `rgb(113,1,61)``\n• #713501\n``#713501` `rgb(113,53,1)``\n• #001425\n``#001425` `rgb(0,20,37)``\n• #01223e\n``#01223e` `rgb(1,34,62)``\n• #012f58\n``#012f58` `rgb(1,47,88)``\n• #013d71\n``#013d71` `rgb(1,61,113)``\n• #014b8a\n``#014b8a` `rgb(1,75,138)``\n• #0158a4\n``#0158a4` `rgb(1,88,164)``\n• #0266bd\n``#0266bd` `rgb(2,102,189)``\nMonochromatic Color\n\n# Alternatives to #013d71\n\nBelow, you can see some colors close to #013d71. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #015971\n``#015971` `rgb(1,89,113)``\n• #015071\n``#015071` `rgb(1,80,113)``\n• #014671\n``#014671` `rgb(1,70,113)``\n• #013d71\n``#013d71` `rgb(1,61,113)``\n• #013471\n``#013471` `rgb(1,52,113)``\n• #012a71\n``#012a71` `rgb(1,42,113)``\n• #012171\n``#012171` `rgb(1,33,113)``\nSimilar Colors\n\n# #013d71 Preview\n\nThis text has a font color of #013d71.\n\n``<span style=\"color:#013d71;\">Text here</span>``\n#013d71 background color\n\nThis paragraph has a background color of #013d71.\n\n``<p style=\"background-color:#013d71;\">Content here</p>``\n#013d71 border color\n\nThis element has a border color of #013d71.\n\n``<div style=\"border:1px solid #013d71;\">Content here</div>``\nCSS codes\n``.text {color:#013d71;}``\n``.background {background-color:#013d71;}``\n``.border {border:1px solid #013d71;}``\n\n# Shades and Tints of #013d71\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #000910 is the darkest color, while #fbfdff is the lightest one.\n\n• #000910\n``#000910` `rgb(0,9,16)``\n• #001323\n``#001323` `rgb(0,19,35)``\n• #001e37\n``#001e37` `rgb(0,30,55)``\n• #01284a\n``#01284a` `rgb(1,40,74)``\n• #01335e\n``#01335e` `rgb(1,51,94)``\n• #013d71\n``#013d71` `rgb(1,61,113)``\n• #014784\n``#014784` `rgb(1,71,132)``\n• #015298\n``#015298` `rgb(1,82,152)``\n• #025cab\n``#025cab` `rgb(2,92,171)``\n• #0267bf\n``#0267bf` `rgb(2,103,191)``\n• #0271d2\n``#0271d2` `rgb(2,113,210)``\n• #027ce6\n``#027ce6` `rgb(2,124,230)``\n• #0286f9\n``#0286f9` `rgb(2,134,249)``\n• #1290fd\n``#1290fd` `rgb(18,144,253)``\n• #2599fd\n``#2599fd` `rgb(37,153,253)``\n• #39a2fd\n``#39a2fd` `rgb(57,162,253)``\n• #4cabfd\n``#4cabfd` `rgb(76,171,253)``\n• #60b4fe\n``#60b4fe` `rgb(96,180,254)``\n• #73bdfe\n``#73bdfe` `rgb(115,189,254)``\n• #87c7fe\n``#87c7fe` `rgb(135,199,254)``\n``#9ad0fe` `rgb(154,208,254)``\n• #aed9fe\n``#aed9fe` `rgb(174,217,254)``\n• #c1e2fe\n``#c1e2fe` `rgb(193,226,254)``\n• #d4ebff\n``#d4ebff` `rgb(212,235,255)``\n• #e8f4ff\n``#e8f4ff` `rgb(232,244,255)``\n• #fbfdff\n``#fbfdff` `rgb(251,253,255)``\nTint Color Variation\n\n# Tones of #013d71\n\nA tone is produced by adding gray to any pure hue. In this case, #36393c is the less saturated color, while #013d71 is the most saturated one.\n\n• #36393c\n``#36393c` `rgb(54,57,60)``\n• #313a41\n``#313a41` `rgb(49,58,65)``\n• #2d3a45\n``#2d3a45` `rgb(45,58,69)``\n• #283a4a\n``#283a4a` `rgb(40,58,74)``\n• #243a4e\n``#243a4e` `rgb(36,58,78)``\n• #203b52\n``#203b52` `rgb(32,59,82)``\n• #1b3b57\n``#1b3b57` `rgb(27,59,87)``\n• #173b5b\n``#173b5b` `rgb(23,59,91)``\n• #133c5f\n``#133c5f` `rgb(19,60,95)``\n• #0e3c64\n``#0e3c64` `rgb(14,60,100)``\n• #0a3c68\n``#0a3c68` `rgb(10,60,104)``\n• #053d6d\n``#053d6d` `rgb(5,61,109)``\n• #013d71\n``#013d71` `rgb(1,61,113)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #013d71 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]

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[ "## Currently displaying 1 – 3 of 3\n\nShowing per page\n\nOrder by Relevance | Title | Year of publication\n\n### An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment\n\nESAIM: Mathematical Modelling and Numerical Analysis\n\nWe consider the system of partial differential equations governing the one-dimensional flow of two superposed immiscible layers of shallow water. The difficulty in this system comes from the coupling terms involving some derivatives of the unknowns that make the system nonconservative, and eventually nonhyperbolic. Due to these terms, a numerical scheme obtained by performing an arbitrary scheme to each layer, and using time-splitting or other similar techniques leads to instabilities in...\n\n### A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport\n\nESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique\n\nThe goal of this paper is to obtain a well-balanced, stable, fast, and robust HLLC-type approximate Riemann solver for a hyperbolic nonconservative PDE system arising in a turbidity current model. The main difficulties come from the nonconservative nature of the system. A general strategy to derive simple approximate Riemann solvers for nonconservative systems is introduced, which is applied to the turbidity current model to obtain two different HLLC solvers. Some results concerning the non-negativity...\n\n### A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport\n\nESAIM: Mathematical Modelling and Numerical Analysis\n\nThe goal of this paper is to obtain a well-balanced, stable, fast, and robust HLLC-type approximate Riemann solver for a hyperbolic nonconservative PDE system arising in a turbidity current model. The main difficulties come from the nonconservative nature of the system. A general strategy to derive simple approximate Riemann solvers for nonconservative systems is introduced, which is applied to the turbidity current model to obtain two different...\n\nPage 1" ]

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[ "# In the methane molecule. CH4, each hydrogen atom is at the corner of a regular tetrahedron with the carbon atom at the center. If one of the CH is in the direction of A=7+7+R and an adjacent C-H bond is at the direction B=1-1-R. results to an angular bond of approximately 109° for a static frozen molecule. However, the molecule we can encounter everyday continuously vibrates and interact with the surrounding causing its bond vector to vary slightly. According to a new spectroscopy analysis, the adjacent bond vectors was found to be A= 0.931 + 0.91) + 1.09k B= 1.02i + -0.99j + -1.08k What is the angle (in degrees) between the bonds based on this new data? Note: Only 1% of error is permitted for the correct answer.\n\nQuestion", null, "help_outlineImage TranscriptioncloseIn the methane molecule. CH4, each hydrogen atom is at the corner of a regular tetrahedron with the carbon atom at the center. If one of the CH is in the direction of A=7+7+R and an adjacent C-H bond is at the direction B=1-1-R. results to an angular bond of approximately 109° for a static frozen molecule. However, the molecule we can encounter everyday continuously vibrates and interact with the surrounding causing its bond vector to vary slightly. According to a new spectroscopy analysis, the adjacent bond vectors was found to be A= 0.931 + 0.91) + 1.09k B= 1.02i + -0.99j + -1.08k What is the angle (in degrees) between the bonds based on this new data? Note: Only 1% of error is permitted for the correct answer. fullscreen\n\n### Want to see this answer and more?\n\nExperts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*\n\n*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.\nTagged in\nScience\nPhysics\n\n### Vectors and Scalars", null, "" ]

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[ "## Using the Right Model Representation\n\nThis example shows some best practices for working with LTI models.\n\n### Which Representation is Best Suited for Computations?\n\nUsing the Control System Toolbox™ software, you can represent LTI systems in four different ways:\n\n• Transfer function (TF)\n\n• Zero-pole-gain (ZPK)\n\n• State space (SS)\n\n• Frequency response data (FRD)\n\nWhile the TF and ZPK representations are compact and convenient for display purposes, they are not ideal for system manipulation and analysis for several reasons:\n\n• Working with TF and ZPK models often results in high-order polynomials whose evaluation can be plagued by inaccuracies.\n\n• The TF and ZPK representations are inefficient for manipulating MIMO systems and tend to inflate the model order.\n\nSome of these limitations are illustrated below. Because of these limitations, you should use the SS or FRD representations for most computations involving LTI models.\n\n### Pitfalls of High-Order Transfer Functions\n\nComputations involving high-order transfer functions can suffer from severe loss of accuracy and even overflow. Even a simple product of two transfer functions can give surprising results, as shown below.\n\nLoad and plot two discrete-time transfer functions `Pd` and `Cd` of order 9 and 2, respectively:\n\n```% Load Pd,Cd models load numdemo Pd Cd % Plot their frequency response bode(Pd,'b',Cd,'r'), grid legend('Pd','Cd')```", null, "Next, compute the open-loop transfer function L = Pd*Cd using the TF, ZPK, SS, and FRD representations:\n\n```Ltf = Pd * Cd; % TF Lzp = zpk(Pd) * Cd; % ZPK Lss = ss(Pd) * Cd; % SS w = logspace(-1,3,100); Lfrd = frd(Pd,w) * Cd; % FRD```\n\nFinally, compare the frequency response magnitude for the resulting four models:\n\n```sigma(Ltf,'b--',Lzp,'g',Lss,'r:',Lfrd,'m--',{1e-1,1e3}); legend('TF','ZPK','SS','FRD')```", null, "The responses from the ZPK, SS, and FRD representations closely match, but the response from the TF representation is choppy and erratic below 100 rad/sec. To understand the loss of accuracy with the transfer function form, compare the pole/zero maps of Pd and Cd near z=1:\n\n```pzplot(Pd,'b',Cd,'r'); title('Pole/zero maps of Pd (blue) and Cd (red)'); axis([0.4 1.05 -1 1])```", null, "Note that there are multiple roots near z=1. Because the relative accuracy of polynomial values drops near roots, the relative error on the transfer function value near z=1 exceeds 100%. The frequencies below 100 rad/s map to `|z-1`|<1e-3, which explains the erratic results below 100 rad/s.\n\n### Pitfalls of Back-and-Forth Conversions Between Representations\n\nYou can easily convert any LTI model to transfer function, zero-pole-gain, or state-space form using the commands `tf`, `zpk`, and `ss`, respectively. For example, given a two-input, two-output random state-space model HSS1 created using\n\n`HSS1 = rss(3,2,2);`\n\nyou can obtain its transfer function using\n\n`HTF = tf(HSS1);`\n\nand convert it back to state-space using\n\n`HSS2 = ss(HTF);`\n\nHowever, beware that such back-and-forth conversions are expensive, can incur some loss of accuracy, and artificially inflate the model order for MIMO systems. For example, the order of `HSS2` is double that of `HSS1` because 6 is the generic order of a 2x2 transfer matrix with denominators of degree 3:\n\n`order(HSS1)`\n```ans = 3 ```\n`order(HSS2)`\n```ans = 6 ```\n\nTo understand the difference in model order, compare the pole/zero maps of the two models:\n\n```subplot(211) pzmap(HSS1,'b') title('Poles and zeros of HSS1'); subplot(212) pzmap(HSS2,'r') title('Poles and zeros of HSS2');```", null, "Notice the cancelling pole/zero pairs in HSS2 depicted by x's inside o's in the pole/zero map. You can use the command `minreal` to eliminate cancelling pole/zero pairs and recover a 3rd-order, minimal state-space model from HSS2:\n\n`HSS2_min = minreal(HSS2);`\n```3 states removed. ```\n`order(HSS2_min)`\n```ans = 3 ```\n\nCheck that `HSS1` and `HSS2_min` coincide by plotting the relative gap between these two models:\n\n```clf Gap = HSS1-HSS2_min; sigma(HSS1,Gap), grid```\n```Warning: The frequency response has poor relative accuracy. This may be because the response is nearly zero or infinite at all frequencies, or because the state-space realization is ill conditioned. Use the \"prescale\" command to investigate further. ```\n`legend('HSS1','Gap HSS1 vs. minimal HSS2','Location','Best')`", null, "The gap (green curve) is very small at all frequencies. Note that `sigma` warns that the `Gap` plot is \"noisy\" because the difference is so small that it essentially consists of rounding errors.\n\nBecause extracting minimal realizations is numerically tricky, you should avoid creating nonminimal models. See also Preventing State Duplication in System Interconnections for related insights." ]

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[ "### 內容目录\n\n#### 上一个主题\n\n< Class Phalcon\\Validation\\Validator\\Alpha\n\n#### 下一个主题\n\nClass Phalcon\\Validation\\Validator\\Callback >\n\nPhalcon玩家群：150237524", null, "# Class Phalcon\\Validation\\Validator\\Between¶\n\nextends abstract class Phalcon\\Validation\\Validator\n\nimplements Phalcon\\Validation\\ValidatorInterface\n\nValidates that a value is between an inclusive range of two values. For a value x, the test is passed if minimum<=x<=maximum.\n\n```<?php\n\nuse Phalcon\\Validation\\Validator\\Between;\n\n\"price\",\nnew Between(\n[\n\"minimum\" => 0,\n\"maximum\" => 100,\n\"message\" => \"The price must be between 0 and 100\",\n]\n)\n);\n\n[\n\"price\",\n\"amount\",\n],\nnew Between(\n[\n\"minimum\" => [\n\"price\" => 0,\n\"amount\" => 0,\n],\n\"maximum\" => [\n\"price\" => 100,\n\"amount\" => 50,\n],\n\"message\" => [\n\"price\" => \"The price must be between 0 and 100\",\n\"amount\" => \"The amount must be between 0 and 50\",\n],\n]\n)\n);\n```\n\n## Methods¶\n\npublic validate (Phalcon\\Validation \\$validation, mixed \\$field)\n\nExecutes the validation\n\npublic __construct ([array \\$options]) inherited from Phalcon\\Validation\\Validator\n\nPhalcon\\Validation\\Validator constructor\n\npublic isSetOption (mixed \\$key) inherited from Phalcon\\Validation\\Validator\n\nChecks if an option has been defined\n\npublic hasOption (mixed \\$key) inherited from Phalcon\\Validation\\Validator\n\nChecks if an option is defined\n\npublic getOption (mixed \\$key, [mixed \\$defaultValue]) inherited from Phalcon\\Validation\\Validator\n\nReturns an option in the validator’s options Returns null if the option hasn’t set\n\npublic setOption (mixed \\$key, mixed \\$value) inherited from Phalcon\\Validation\\Validator\n\nSets an option in the validator" ]

[ null, "http://pub.idqqimg.com/wpa/images/group.png", null ]

[ "# 9.6: 9.2 Managing the Budget -- Project Management for Instructional Designers\n\n## 9.2 Managing the Budget\n\nVisit Audio Recordings for the audio version of this section.\n\n###### LEARNING OBJECTIVES\n1. Describe methods to manage cash flow.\n2. Describe the terms and relationships of budget factors used in earned value analysis.\n3. Calculate and interpret budget and schedule variances.\n4. Calculate and interpret the schedule performance index and the cost performance index.\n5. Calculate and interpret estimates to complete the project.\n6. Calculate the revised final budget.\n\nProjects seldom go according to plan in every detail. It is necessary for the project manager to be able to identify when costs are varying from the budget and to manage those variations.\n\n#### MANAGING CASH FLOW\n\nIf the total amount spent on a project is equal to or less than the amount budgeted, the project can still be in trouble if the funding for the project is not available when it is needed. There is a natural tension between the financial people in an organization, who do not want to pay for the use of money that is just sitting in a checking account, and the project manager, who wants to be sure that there is enough money available to pay for project expenses. The financial people prefer to keep the company’s money working in other investments until the last moment before transferring it to the project account. The contractors and vendors have similar concerns, and they want to get paid as soon as possible so they can put the money to work in their own organizations. The project manager would like to have as much cash available as possible to use if activities exceed budget expectations.\n\n##### Contingency Reserves\n\nMost projects have something unexpected occur that increases costs above the original estimates. If estimates are rarely exceeded, the estimating method should be reviewed because the estimates are too high. It is impossible to predict which activities will cost more than expected, but it is reasonable to assume that some of them will. Estimating the likelihood of such events is part of risk analysis, which is discussed in more detail in a later chapter.\n\nInstead of overestimating each cost, money is budgeted for dealing with unplanned but statistically predictable cost increases. Funds allocated for this purpose are called contingency reserves.1 Because it is likely that this money will be spent, it is part of the total budget for the project. If this fund is adequate to meet the unplanned expenses, then the project will complete within the budget.\n\n##### Management Reserves\n\nIf something occurs during the project that requires a change in the project scope, money may be needed to deal with the situation before a change in scope can be negotiated with the project sponsor or client. It could be an opportunity as well as a challenge. For example, if a new technology were invented that would greatly enhance your completed project, there would be additional cost and a change to the scope, but it would be worth it. Money can be made available at the manager’s discretion to meet needs that would change the scope of the project. These funds are called management reserves. Unlike contingency reserves, they are not likely to be spent and are not part of the project’s budget baseline, but they can be included in the total project budget.2\n\n#### Evaluating the Budget During the Project\n\nA project manager must regularly compare the amount of money spent with the budgeted amount and report this information to managers and stakeholders. It is necessary to establish an understanding of how this progress will be measured and reported.\n\n###### Reporting Budget Progress on John’s Move\nIn the John’s move example, he estimated that the move would cost about $1,500 and take about sixteen days. Eight days into the project, John has spent$300. John tells his friends that the project is going well because he is halfway through the project but has only spent a fifth of his budget. John’s friend Carlita points out that his report is not sufficient because he did not compare the amount spent to the budgeted amount for the activities that should be done by the eighth day.\n\nAs John’s friend points out, a budget report must compare the amount spent with the amount that is expected to be spent by that point in the project. Basic measures such as percentage of activities completed, percentage of measurement units completed, and percentage of budget spent are adequate for less complex projects, but more sophisticated techniques are used for projects with higher complexity.\n\n#### EARNED VALUE ANALYSIS\n\nA method that is widely used for medium- and high-complexity projects is the earned value management (EVM) method. EVM is a method of periodically comparing the budgeted costs with the actual costs during the project. It combines the scheduled activities with detailed cost estimates of each activity. It allows for partial completion of an activity if some of the detailed costs associated with the activity have been paid but others have not.\n\nThe budgeted cost of work scheduled (BCWS) comprises the detailed cost estimates for each activity in the project. The amount of work that should have been done by a particular date is the planned value (PV). These terms are used interchangeably by some sources, but the planned value term is used in formulas to refer to the sum of the budgeted cost of work up to a particular point in the project, so we will make that distinction in the definitions in this text for clarity.\n\n###### Planned Value on Day Six of John’s Move\nOn day six of the project, John should have taken his friends to lunch and purchased the packing materials. The portion of the BCWS that should have been done by that date (the planned value) is listed in Figure 9.6. This is the planned value for day six of the project.\n##### Figure 9.6 Planned Value for Lunch and Packing Materials", null, "The budgeted cost of work performed (BCWP) is the budgeted cost of work scheduled that has been done. If you sum the BCWP values up to that point in the project schedule, you have the earned value (EV). The amount spent on an item is often more or less than the estimated amount that was budgeted for that item. The actual cost (AC) is the sum of the amounts actually spent on the items.\n\n###### Comparing PV, EV, and AC in John’s Move on Day Six\nDion and Carlita were both trying to lose weight and just wanted a nice salad. Consequently, the lunch cost less than expected. John makes a stop at a store that sells moving supplies at discount rates. They do not have all the items he needs, but the prices are lower than those quoted by the moving company. They have a very good price on lifting straps so he decides to buy an extra pair. He returns with some of the items on his list, but this phase of the job is not complete by the end of day six. John bought half of the small boxes, all of five other items, twice as many lifting straps, and none of four other items. John is only six days into his project, and his costs and performance are starting to vary from the plan. Earned value analysis gives us a method for reporting that progress (refer to Figure 9.7).\n##### Figure 9.7 Planned Value, Earned Value, and Actual Cost", null, "##### Variance Indexes for Schedule and Cost\n\nThe schedule variance and the cost variance provide the amount by which the spending is behind (or ahead of) schedule and the amount by which a project is exceeding (or less than) its budget. They do not give an idea of how these amounts compare with the total budget.\n\nThe ratio of earned value to planned value gives an indication of how much of the project is completed. This ratio is the schedule performance index (SPI). The formula is SPI = EV/PV. In the John’s move example, the SPI equals 0.62 (SPI = $162.10/$261.65 = 0.62) A SPI value less than one indicates the project is behind schedule.\n\nThe ratio of the earned value to the actual cost is the cost performance index (CPI). The formula is CPI = EV/AC.\n\n###### Cost Performance Index of John’s Move\n\nIn the John’s move example, CPI = $162.10/$154.50 = 1.05 A value greater than 1 indicates the project is under budget.\n\n##### Figure 9.8 Schedule Variance and Cost Variance on Day Six of the John’s Move Project", null, "The cost variance of positive $7.60 and the CPI value of 1.05 tell John that he is getting more value for his money than planned for the tasks scheduled by day six. The schedule variance (SV) of negative$99.55 and the schedule performance index (SPI) of 0.62 tell him that he is behind schedule in adding value to the project.\n\nDuring the project, the manager can evaluate the schedule using the schedule variance (SV) and the schedule performance index (SPI) and the budget using the cost variance (CV) and the cost performance index (CPI).\n\n#### ESTIMATED COST TO COMPLETE THE PROJECT\n\nPartway through the project, the manager evaluates the accuracy of the cost estimates for the activities that have taken place and uses that experience to predict how much money it will take to complete the unfinished activities of the project—the estimate to complete (ETC).\n\nTo calculate the ETC, the manager must decide if the cost variance observed in the estimates to that point are representative of the future. For example, if unusually bad weather causes increased cost during the first part of the project, it is not likely to have the same effect on the rest of the project. If the manager decides that the cost variance up to this point in the project is atypical—not typical—then the estimate to complete is the difference between the original budget for the entire project—the budget at completion (BAC)—and the earned value (EV) up to that point. Expressed as a formula, ETC = BAC − EV\n\n###### Estimate to Complete John’s Move\nIn John’s move, John was able to buy most of the items at a discount house that did not have a complete inventory and, he chose to buy an extra pair of lift straps. He knows that the planned values for packing materials were obtained from the price list at the moving company where he will have to buy the rest of the items, so those two factors are not likely to be typical of the remaining purchases. The reduced cost of lunch is unrelated to the future costs of packing materials, truck rentals, and hotel fees. John decides that the factors that caused the variances are atypical. He calculates that the estimate to complete (ETC) is the budget at completion ($1,534) minus the earned value at that point ($162.10), which equals $1,371.90. Expressed as a formula, ETC =$1,534 − $162.10 =$1,371.90.\n\nIf the manager decides that the cost variance is caused by factors that will affect the remaining activities, such as higher labor and material costs, then the estimate to complete (ETC) needs to be adjusted by dividing it by the cost performance index (CPI). For example, if labor costs on the first part of a project are estimated at $80,000 (EV) and they actually cost$85,000 (AC), the cost variance will be 0.94. (Recall that the cost variance = EV/AC).\n\nTo calculate the estimate to complete (ETC) assuming the cost variance on known activities is typical of future cost, the formula is ETC = (BAC – EV)/CPI. If the budget at completion (BAC) of the project is $800,000, the estimate to complete is ($800,000 – $80,000)/0.94 =$766,000.\n\n#### ESTIMATE FINAL PROJECT COST\n\nIf the costs of the activities up to the present vary from the original estimates, it will affect the total estimate for the project cost. The new estimate of the project cost is the estimate at completion (EAC). To calculate the EAC, the estimate to complete (ETC) is added to the actual cost (AC) of the activities already performed. Expressed as a formula, EAC = AC + ETC.\n\n###### Estimate at Completion for John’s Move\nThe revised estimate at completion (EAC) for John’s move at this point in the process is EAC = $154.50 +$1,371.90 = \\$1,526.40.\n\nRefer to Figure 9.9 for a summary of terms and formulas.\n\n##### Figure 9.9 Summary of Terms and Formulas for Earned Value Analysis", null, "###### KEY TAKEAWAYS\n• Extra money is allocated in a contingency fund to deal with activities where costs exceed estimates. Funds are allocated in a management reserves in case a significant opportunity or challenge occurs that requires change of scope but funds are needed immediately before a scope change can typically be negotiated.\n• Schedule variance is the difference between the part of the budget that has been done so far (EV) versus the part that was planned to be completed by now (PV). Similarly, the cost variance is the difference between the EV and the actual cost (AC).\n• The schedule performance index (SPI) is the ratio of the earned value and the planned value. The cost performance index (CPI) is the ratio of the earned value (EV) to the actual cost (AC).\n• The formula used to calculate the amount of money needed to complete the project (ETC) depends on whether or not the cost variance to this point is expected to continue (typical) or not (atypical). If the cost variance is atypical, the ETC is simply the original total budget (BAC) minus the earned value (EV). If they are typical of future cost variances, the ETC is adjusted by dividing the difference between BAC and EV by the CPI.\n• The final budget is the actual cost (AC) to this point plus the estimate to complete (ETC).\n\n Project Management Institute, Inc., A Guide to the Project Management Body of Knowledge (PMBOK Guide), 4th ed. (Newtown Square, PA: Project Management Institute, Inc., 2008), 173.\n\n Project Management Institute, Inc., A Guide to the Project Management Body of Knowledge (PMBOK Guide), 4th ed. (Newtown Square, PA: Project Management Institute, Inc., 2008), 177." ]

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[ "", null, "# Colleges with the lowest SAT scores in North Dakota\n\nTop 5 colleges in North Dakota with the lowest SAT scores\nLooking for the colleges with the lowest SAT scores in North Dakota? Well you're in luck! We've compiled a national college database and have created a list of the top 5 universities with the lowest SAT scores in North Dakota below. If you are not a good test taker or worried about your test scores, this list is for you. These are the schools whose applicants had the lowest average SAT scores in North Dakota, which means that you can get into these colleges with a lower SAT score. We also include each college's ACT scores and acceptance rate so that you can see where you would have the easiest time getting in. Read on to find out more.\n\n## Valley City State University SAT scores\n\nThe average SAT score for Valley City State University is 1024.", null, "", null, "The average SAT score of 1024 breaks down into:\n\n• SAT math: 520\n\nThe average ACT score for Valley City State University is 21 and their acceptance rate is 73.7%.\n\n## Minot State University SAT scores\n\nThe average SAT score for Minot State University is 1030.", null, "", null, "The average SAT score of 1030 breaks down into:\n\n• SAT math: 520\n\nThe average ACT score for Minot State University is 22 and their acceptance rate is 50.1%.\n\n## Mayville State University SAT scores\n\nThe average SAT score for Mayville State University is 1040.", null, "", null, "The average SAT score of 1040 breaks down into:\n\n• SAT math: 520\n\nThe average ACT score for Mayville State University is 20 and their acceptance rate is 57.1%.\n\n## University of North Dakota SAT scores\n\nThe average SAT score for University of North Dakota is 1110.", null, "", null, "The average SAT score of 1110 breaks down into:\n\n• SAT math: 570\n\nThe average ACT score for University of North Dakota is 23 and their acceptance rate is 82.2%.\n\n## North Dakota State University SAT scores\n\nThe average SAT score for North Dakota State University is 1170.", null, "", null, "The average SAT score of 1170 breaks down into:\n\n• SAT math: 590" ]

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[ "# Hexagram Navigator", null, "## Contrast Cluster\n\nThis cluster satisfies the equation ~P = o(P). Specifically, it satisfies ~P = o(P) and ~P ≠ e(P).", null, "A: A = e(~B) A = ~C = o(C) A = e(D)", null, "B: B = e(~A) B = ~D = o(D) B = e(C)", null, "C: C = e(~D) C = ~A = o(A) C = e(B)", null, "D: D = e(~C) D = ~B = o(B) D = e(A)\n\nThis cluster has the same key opposition relationships as the Canonical Taiji Contrast Cluster obeying the equation X = e(~Y) for distinct X and Y, but makes ~(.) and o(.) the same rather than equating e(.) and o(.) as the canonical cluster does. In both cases, this prevents discussion of reflection as a distinct operation." ]

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[ "# 7.4: The Extended Mk Model\n\n•", null, "• Contributed by Luke J. Harmon\n• Professor (Biological Sciences) at University of Idaho\n\nThe Mk model assumes that transitions among all possible character states occur at the same rate. However, that may not be a valid assumption. For example, it is often supposed that it is easier to lose a complex character than to gain one. We might want to fit models that allow for such asymmetries in rates.\n\nFor models of DNA sequence evolution there are a wide range of models allowing different rates between distinct types of nucleotides (Yang 2006). Unequal rates are usually incorporated into the Mk model in two ways. First, one can consider the symmetric model (SYM; Paradis et al. 2004). In the symmetric model, the rate of change between any two character states is the same forwards as it is backwards (that is, rates of change are symmetric; qij = qji). The rate for a particular pair of states might differ from other pairs of character states. Note that when k = 2 the symmetric model is identical to the basic Mk model. The rate matrix for this model has as many free rate parameters as there are pairs of character states:\n\n(eq. 7.11)\n\n$$p = \\frac{k(k-1)}{2}$$\n\nHowever, in general symmetric models will not have stationary distributions where all character states occur at equal frequencies, as noted above for the Mk model. We can account for these uneven frequencies by adding additional parameters to our model:\n\n(eq. 7.12)\n\n$$\\pi_{SYM} = \\begin{bmatrix} \\pi_1 & \\pi_2 & \\dots & 1 - \\sum_{i=1}^{n-1} \\pi_i \\end{bmatrix}$$\n\nNote that we only have to specify n − 1 equilibrium frequencies, since we know that they all sum to one. We have added n − 1 new parameters, for a total number of parameters:\n\n(eq. 7.13)\n\n$$p = \\frac{k(k-1)}{2} + n-1$$\n\nTo obtain a Q-matrix for this model, we combine the information from both the relative transition rates and equilibrium frequencies:\n\n(eq. 7.14)\n\n$$\\mathbf{Q} = \\begin{bmatrix} \\cdot & r_1 & \\dots & r_{n-1} \\\\ r_1 & \\cdot & \\dots & \\vdots \\\\ \\vdots & \\vdots & \\cdot & r_{k(k-1)/2} \\\\ r_{n-1} & \\dots & r_{k(k-1)/2} & \\cdot \\\\ \\end{bmatrix} \\begin{bmatrix} \\pi_1 & 0 & 0 & 0 \\\\ 0 & \\pi_2 & 0 & 0 \\\\ 0 & 0 & \\ddots & 0 \\\\ 0 & 0 & 0 & \\pi_n \\\\ \\end{bmatrix}$$\n\nIn this equation I have left the diagonal of the first matrix as dots. The final Q-matrix must have all rows sum to one, so one can adjust the values of that matrix after the multiplication step.\n\nIn the case of a two-state model, for example, we can create a model where the forward rate is double the backward rate, and the equilibrium frequency of character one is 0.75. Then:\n\n(eq. 7.15)\n\n$$\\mathbf{Q} = \\begin{bmatrix} \\cdot & 1 \\\\ 2 & \\cdot \\\\ \\end{bmatrix} \\begin{bmatrix} 0.75 & 0 \\\\ 0 & 0.25 \\\\ \\end{bmatrix} = \\begin{bmatrix} \\cdot & 0.25 \\\\ 1.5 & \\cdot \\\\ \\end{bmatrix} = \\begin{bmatrix} -0.25 & 0.25 \\\\ 1.5 & -1.5 \\\\ \\end{bmatrix}$$\n\nIt is worth noting that this approach of setting parameters that define equilibrium state frequences, although borrowed from molecular evolution, is not completely standard in the comparative methods literature. One also sees equilibrium frequencies treated as a fixed property of the model, and assumed to be either equal across states or tied directly to the parameters in the Q-matrix.\n\nThe second common extension of the Mk model is called the all-rates-different model (ARD; Paradis et al. 2004). In this model every possible type of transition can have a different rate. There are thus k(k − 1) free rate parameters for this model, and again n − 1 parameters to specify the equilibrium frequencies of the character states.\n\nThe same algorithm can be used to calculate the likelihood for both of these extended Mk models (SYM and ARD). These models have more parameters than the standard Mk. To find maximum likelihood solutions, we must optimize the likelihood across the entire set of unknown parameters (see Chapter 7)." ]

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[ "", null, "## Index for surnames beginning with n (Family Pages)[Nalevykin, George ] - [Noakes, Thomas ]\n\nFor privacy reasons, Date of Birth and Date of Marriage for persons believed to still be living are not shown.\n\nA B C D E F G H I J K L M N O P Q R S T U V W X Y Z (NONE/OTHER)\n\n[Nalevykin, George ] - [Noakes, Thomas ]\n[Nobbs, Elizabeth ] - [Nye, Ann ]\n[Nye, Dive ] - [Nye, William Dunster ]\n\n### Back to Main Page\n\nNalevykin, George (b. 05 FEB 1895 - d. 13 AUG 1984)\nNash, Annie Maria (b. 1865 - d. 1926)\nNash, Clara (b. 1890 - d. 1894)\nNash, Edmond (b. 1840 - d. 1883)\nNash, Edward Millen (b. 1843 - d. BTW 1881 - 1891)\nNash, Jane (b. 1848 - d. 1939)\nNash, John (b. 1847 - d. 1923)\nNayler, Anne (b. 1834 - d. -)\nNeale, Elizabeth\nNeale, Rosina M (b. 1914 - d. 1953)\nNealen, Henry (b. 1866 - d. -)\nNealen, James\nNeame, C\nNeame, John\nNeame, William\nNeave, Sophia H (b. 1898 - d. 1968)\nNeaves, John\nNeeve, Ann (b. 1793 - d. 1848)\nNeeve, Harriet (b. 1827 - d. 1889)\nNeeves, Albert (b. 26 JUL 1895 - d. 01 JAN 1959)\nNeeves, Annie (b. 27 APR 1905 - d. 21 MAR 1991)\nNeeves, Edgar (b. 1898 - d. 1898)\nNeeves, Ellen (b. 15 MAY 1893 - d. 12 APR 1974)\nNeeves, Ernest James (b. 1901 - d. -)\nNeeves, George (b. 1894 - d. 1894)\nNeeves, George Thomas (b. 27 AUG 1927 - d. 01 MAY 1992)\nNeeves, Horace Victor (b. 01 DEC 1899 - d. 08 JAN 1969)\nNeeves, James (b. 1861 - d. 19 FEB 1929)\nNeeves, Lewis (b. 19 MAR 1897 - d. 20 DEC 1973)\nNeeves, Lydia\nNeeves, Martha\nNell, Martha (b. 1787 - d. -)\nNell, Mary (b. 1789 - d. -)\nNell, Sarah (b. 1793 - d. -)\nNell, Thomas (b. 22 JAN 1796 - d. -)\nNell, Thomas (d. 1807)\nNell, William (b. 1799 - d. -)\nNelson, Charles Herbert (b. 1881)\nNethersell, Irene Clarrisa (b. 02 MAR 1905 - d. 1980)\nNeve, George\nNew, Ann (b. 1860 - d. -)\nNew, Edward (b. 24 NOV 1835 - d. 1913)\nNew, George (b. 1820 - d. -)\nNew, Henry (b. 1857 - d. -)\nNew, Lucy Ann (b. 1851 - d. 1921)\nNewberry, Harriett (b. 1815 - d. -)\nNewble, Lydia (b. 1822 - d. -)\nNewdick, Herbert Edwin (b. 09 APR 1905 - d. 1982)\nNewell, Douglas Frederick Gordon (b. 1919 - d. 1976)\nNewell, Elizabeth (b. 1849 - d. -)\nNewing, Edwin (b. 1865 - d. 1934)\nNewing, Elizabeth (b. 1858 - d. 1885)\nNewing, James (b. 1827 - d. 1906)\nNewing, Rachel (b. 1834 - d. 1914)\nNewing, Robert\nNewing, Robert\nNewington, Alice (b. 23 AUG 1866 - d. -)\nNewington, Anne (b. 1822 - d. 1917)\nNewington, Benjamin (b. 1786 - d. -)\nNewington, Elizabeth\nNewington, Emily Elizabeth Mary (b. 31 JAN 1883 - d. 1959)\nNewington, Frances Alice (b. 1889)\nNewington, James Percy (b. 15 JUL 1887 - d. 22 FEB 1919)\nNewington, Peter Charles (b. 1856 - d. 1911)\nNewington, Sarah (b. 10 MAR 1792)\nNewington, Thomas Peter (b. 13 AUG 1885 - d. 1956)\nNewington, Valentine (b. 1756 - d. 1813)\nNewis, Avis (b. 1781 - d. 1865)\nNewlands, Mary\nNewlyn, E\nNewmam, John\nNewman, Edward (b. 1809 - d. 1886)\nNewman, Emma (b. 1842 - d. 1927)\nNewman, Harriet Elizabeth (b. 1838 - d. 1915)\nNewman, James\nNewman, Lydia (b. 1825 - d. 1883)\nNewport, Ann (b. 1646 - d. 1720)\nNewport, Ann (b. 1884 - d. 1957)\nNewport, Ann (b. 1680 - d. -)\nNewport, Edward (b. 1754 - d. -)\nNewport, Elizabeth (b. 1812 - d. 1895)\nNewport, Elizabeth (b. 27 SEP 1648 - d. -)\nNewport, Elizabeth (b. 1674 - d. -)\nNewport, Emily (b. 1887 - d. -)\nNewport, Esther (b. 1879 - d. 1941)\nNewport, Francis Louis (b. 16 JUN 1910 - d. 1995)\nNewport, James (b. 1896 - d. 1964)\nNewport, James (b. 1753 - d. -)\nNewport, John (b. 1782)\nNewport, John\nNewport, John (b. 1644 - d. 1719)\nNewport, John (b. 1858 - d. 1933)\nNewport, John (b. 31 OCT 1881 - d. -)\nNewport, John James (b. 1869 - d. 1932)\nNewport, Martha (b. 1658 - d. -)\nNewport, Mary (b. 1662 - d. 1666)\nNewport, Mary\nNewport, Myria\nNewport, Peter Louis (b. 19 FEB 1932 - d. 2000)\nNewport, Sara (b. 1661)\nNewport, Sarah (b. 1787)\nNewport, Sarah (b. 1850)\nNewport, Susan (b. 1653 - d. 1676)\nNewport, William (b. 1892 - d. -)\nNewport, William (b. 1650 - d. -)\nNewport, William (b. 1683 - d. -)\nNewport, William (b. 1618 - d. 1688)\nNewton, Charlotte (b. 1841 - d. -)\nNewton, Edward (b. 1855 - d. 23 JUL 1917)\nNewton, Elizabeth Ann (b. 1852 - d. -)\nNewton, Florence Beatrice\nNewton, Gwendoline\nNewton, Harold Leonard (b. 1900 - d. -)\nNewton, Harriet (b. 1857 - d. -)\nNewton, Harriet Ann\nNewton, Harriett (b. 1888 - d. -)\nNewton, Isaac (b. 1785 - d. 1844)\nNewton, Isaac (b. 20 JUL 1808 - d. 1809)\nNewton, Isaac (b. 1843 - d. -)\nNewton, John (b. 1838 - d. -)\nNewton, John Cavel (b. 1850 - d. -)\nNewton, Leonard Charles (b. 1906 - d. -)\nNewton, Leonard Henry (b. 1867 - d. -)\nNewton, Mabel Julia (b. 1882 - d. -)\nNewton, Mary (b. 1836 - d. -)\nNewton, Richard (b. 1883 - d. -)\nNewton, Sarah a (b. 1845 - d. -)\nNewton, Thomas Cavel (b. 1847 - d. -)\nNewton, Walter Edward (b. 1880 - d. 01 MAY 1961)\nNewton, Walter Edward\nNewton, Wilfred Edward (b. 04 MAR 1901 - d. 1980)\nNewton, William (b. 1812 - d. 1856)\nNewton, William Henry (b. 1834 - d. 1895)\nNicholls, Abraham (b. 1834 - d. 1925)\nNicholls, Abraham John (b. 08 AUG 1899 - d. 1972)\nNicholls, Alfred Edward (b. 1868 - d. 1943)\nNicholls, Alfred James (b. 11 OCT 1895 - d. 1967)\nNicholls, Bernard (b. 1905 - d. -)\nNicholls, Bertha Agnes (b. 1880 - d. -)\nNicholls, Charles Edward (b. 1901 - d. 1961)\nNicholls, Charles Edward (b. 03 DEC 1893 - d. 1970)\nNicholls, Charles Robert (b. 1878 - d. 1942)\nNicholls, Doreen Muriel (b. 1904 - d. -)\nNicholls, Edith Bertha (b. 09 APR 1909 - d. 1989)\nNicholls, Elizabeth Maria (b. 1861 - d. 1943)\nNicholls, Ellen (b. 1839 - d. -)\nNicholls, Ellen Fanny (b. 1866 - d. 1952)\nNicholls, Frances Ann (b. 1836 - d. 1909)\nNicholls, George (b. 1833 - d. 1902)\nNicholls, Isabell Jane (b. 1872 - d. 1968)\nNicholls, James (b. 1798 - d. 1873)\nNicholls, Jane (b. 1825 - d. -)\nNicholls, John (b. 1843 - d. -)\nNicholls, John (b. 1820 - d. 1831)\nNicholls, Joyce Kathleen (b. 03 NOV 1904 - d. 1974)\nNicholls, Lawrence Alfred (b. 1903 - d. 1968)\nNicholls, Louisa Mary (b. 22 AUG 1905 - d. 1980)\nNicholls, Louisa Mary (b. 1874 - d. 1950)\nNicholls, Mabel Pankhurst (b. 1882 - d. 27 MAY 1935)\nNicholls, Maria (b. 1829 - d. 1887)\nNicholls, Maria Anne (b. 1863 - d. 1951)\nNicholls, Peter Conway (b. 30 MAY 1928 - d. 1996)\nNicholls, Phoebe (b. 1783 - d. 1854)\nNicholls, Phoebe (b. 1828 - d. -)\nNicholls, Rupert (b. 1880 - d. 1926)\nNicholls, Sarah (b. 1827 - d. 1893)\nNicholls, Sarah (b. 1748 - d. -)\nNicholls, Thomas (b. 1832 - d. -)\nNicholls, Thomas Abraham (b. 1865 - d. 1865)\nNicholls, William Oliver (b. 1871 - d. 1947)\nNichols, Doris Audry (b. 1906 - d. -)\nNichols, John (b. 1876 - d. -)\nNickolls, Cecil Fleetwood (b. 1900 - d. -)\nNickolls, Frank Robert Manoah (b. 01 JUL 1908 - d. 26 DEC 1974)\nNickolls, Thomas\nNighingale, Katherine\nNightingale, Charles (b. 1866 - d. -)\nNightingale, Emily\nNightingale, John T (b. 10 APR 1844 - d. 28 MAY 1909)\nNightingale, Millicent E (b. 1897 - d. -)\nNightingale, Thomas (b. 1816 - d. 1862)\nNightingale, Walter C A (b. 1899 - d. -)\nNightingale, Wilfred B J (b. 1900 - d. -)\nNinn, Elizabeth (d. 1777)\nNinnes, James W E (b. 1917 - d. -)\nNinnes, Rose L (b. 1920 - d. -)\nNinnes, Stephen James Edward (b. 1893 - d. 1953)\nNix, Carolyn\nNoakes, Cecila (b. 1835 - d. 10 JUL 1867)\nNoakes, Elizabeth\nNoakes, Frederick (b. 1851)\nNoakes, Hannah (b. 1796 - d. 1859)\nNoakes, Harriet Ann (b. 1877 - d. -)\nNoakes, Isaac\nNoakes, Martha (b. 1838)\nNoakes, Mary Fairal (b. 1759 - d. 1821)\nNoakes, Mary Jane (b. 1828 - d. 1872)\nNoakes, Samuel\nNoakes, Sophia\nNoakes, Thomas\n\nThis HTML database was produced by a registered copy of", null, "GED4WEB© version 3.32 ." ]

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[ "# Convert Excel Sheet to a High-Resolution Image in C#, VB.NET\n\nSometimes, you may want to convert Excel sheet to a high-resolution image, especially when the Excel report contains graphs or pictures. This article will show you how to set image resolution when saving Excel sheet to JPG using Spire.XLS.\n\nStep 1: Create a custom function that you can use to reset the image resolution.\n\n```private static Bitmap ResetResolution(Metafile mf, float resolution)\n{\nint width = (int)(mf.Width * resolution / mf.HorizontalResolution);\nint height = (int)(mf.Height * resolution / mf.VerticalResolution);\nBitmap bmp = new Bitmap(width, height);\nbmp.SetResolution(resolution, resolution);\nGraphics g = Graphics.FromImage(bmp);\ng.DrawImage(mf, 0, 0);\ng.Dispose();\nreturn bmp;\n}\n```\n\nStep 2: Create a workbook instance and load the sample Excel file.\n\n```Workbook workbook = new Workbook();\n```\n\nStep 3: Get the worksheet you want to convert.\n\n```Worksheet worksheet = workbook.Worksheets;\n```\n\nStep 4: Convert the worksheet to EMF stream.\n\n```MemoryStream ms = new MemoryStream();\nworksheet.ToEMFStream(ms, 1, 1, worksheet.LastRow, worksheet.LastColumn);\n```\n\nStep 5: Create an image from the EMF stream, and call ResetResolution to reset the resolution for the image.\n\n```Image image = Image.FromStream(ms);\nBitmap images = ResetResolution(image as Metafile, 300);\n```\n\nStep 6: Save the image in JPG file format.\n\n```images.Save(\"Result.jpg\", ImageFormat.Jpeg);\n```\n\nOutput:", null, "Full Code:\n\n[C#]\n```using Spire.Xls;\nusing System.Drawing;\nusing System.Drawing.Imaging;\nusing System.IO;\nnamespace Convert\n{\nclass Program\n{\nstatic void Main(string[] args)\n{\nWorkbook workbook = new Workbook();\nWorksheet worksheet = workbook.Worksheets;\n\nusing (MemoryStream ms = new MemoryStream())\n{\n\nworksheet.ToEMFStream(ms, 1, 1, worksheet.LastRow, worksheet.LastColumn);\nImage image = Image.FromStream(ms);\nBitmap images = ResetResolution(image as Metafile, 300);\nimages.Save(\"Result.jpg\", ImageFormat.Jpeg);\n}\n}\nprivate static Bitmap ResetResolution(Metafile mf, float resolution)\n{\nint width = (int)(mf.Width * resolution / mf.HorizontalResolution);\nint height = (int)(mf.Height * resolution / mf.VerticalResolution);\nBitmap bmp = new Bitmap(width, height);\nbmp.SetResolution(resolution, resolution);\nGraphics g = Graphics.FromImage(bmp);\ng.DrawImage(mf, 0, 0);\ng.Dispose();\nreturn bmp;\n}\n}\n}\n```\n[VB.NET]\n```Imports Spire.Xls\nImports System.Drawing\nImports System.Drawing.Imaging\nImports System.IO\nNamespace Convert\nClass Program\nPrivate Shared Sub Main(args As String())\nDim workbook As New Workbook()\nDim worksheet As Worksheet = workbook.Worksheets(0)\n\nUsing ms As New MemoryStream()\n\nworksheet.ToEMFStream(ms, 1, 1, worksheet.LastRow, worksheet.LastColumn)\nDim image__1 As Image = Image.FromStream(ms)\nDim images As Bitmap = ResetResolution(TryCast(image__1, Metafile), 300)\nimages.Save(\"Result.jpg\", ImageFormat.Jpeg)\nEnd Using\nEnd Sub\nPrivate Shared Function ResetResolution(mf As Metafile, resolution As Single) As Bitmap\nDim width As Integer = CInt(mf.Width * resolution / mf.HorizontalResolution)\nDim height As Integer = CInt(mf.Height * resolution / mf.VerticalResolution)\nDim bmp As New Bitmap(width, height)\nbmp.SetResolution(resolution, resolution)\nDim g As Graphics = Graphics.FromImage(bmp)\ng.DrawImage(mf, 0, 0)\ng.Dispose()\nReturn bmp\nEnd Function\nEnd Class\nEnd Namespace\n```", null, "" ]

[ null, "https://cdn.e-iceblue.com/images/art_images/Convert-Excel-Sheet-to-a-High-Resolution-Image.png", null, "https://cdn.e-iceblue.com/components/com_docs/images/loading.gif", null ]

[ "# Problem 737\n\nFind the sum of the first five terms of the arithmetic series:\n\nan = 2n +2.\n\nSolution:-\n\nFind a1 and  a5  and use the formula for the sum of an arithmetic series:    Sn =", null, "(a1 + an)\n\na1 = 2* 1 + 2 = 4\n\na5 =2*5 +2 = 12\n\nSn = 40" ]

[ null, "https://mymathangels.com/wp-content/ql-cache/quicklatex.com-a8a35e021deb049d8d0fbe27ce285385_l3.png", null ]

[ "# baby-step, giant-step vs Pollard-rho\n\nI'm studying algorithms that solve the discrete logarithm problem over elliptic curve. Reading online, it seems that people use the bsgs algorithm when the order of the curve is \"low\" and P-rho when it's \"high\".\n\nBut nobody says how much is \"low\" and \"high\", where I can find some good estimation? Is this true?\n\n• It appears that Pollard-Rho is a (little) bit harder to implement than BSGS. Can you give example(s) of BSGS being \"preferred\" for \"small\" orders?\n– SEJPM\nJan 31 '18 at 18:52\n\nSo, finding an estimation depends on how much memory is available for you. Since you need to store all the generated points in a hash table for BSGS. If each point requires k-bits of storage and the curve is of order n, the storage requirement is $k * \\sqrt{n}$ bits.\nEg: If each points require 32 bits of storage and the curve has order $10^9$ then total storage requirement is approxmiately 4 GB." ]

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[ "# TALK: JM Landsberg: Geometry and the Complexity of Matrix Multiplication\n\nWednesday, April 29, 2015 - 4:00pm to 5:00pm\nLocation:\n32-G575\nSpeaker:\nJM Landsberg\nBiography:\nTexas A&M\n\nEver since Strassen showed that nxn matrices can be multiplied using O(n^2.81) arithmetic operations as opposed to the usual\nO(n^3), there has been substantial research to determine just how efficiently matrices can be multiplied. This has led to the astounding conjecture that asymptotically, it is nearly as easy to multiply matrices as it is to add them, more precisely,  that matrices can be multiplied using O(n^{2+s}) arithmetic operations for any s>0.\n\nI will explain how geometry has been useful in proving lower complexity bounds, and describe very recent work that indicates\nhow geometry may also be used to prove upper bounds.\n\nThis is joint work with L. Chiantini, C. Ikenmeyer, G. Ottaviani and M. Michalek." ]

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[ "# What is 1/9 of 47?\n\n## What is 1 / 9 of 47 and how to calculate it yourself\n\n1 / 9 of 47 = 5.22\n\n1 / 9 of 47 is 5.22. In this article, we will go through how to calculate 1 / 9 of 47 and how to calculate any fraction of any whole number (integer). This article will show a general formula for solving this equation for positive numbers, but the same rules can be applied for numbers less than zero too!\n\nLet’s dive into how to solve!\n\n### 1: First step in solving 1 / 9 of 47 is understanding your fraction\n\n1 / 9 has two important parts: the numerator (1) and the denominator (9). The numerator is the number above the division line (called the vinculum) which represent the number of parts being taken from the whole. For example: If there were 14 cars total and 1 painted red, 1 would be the numerator or parts of the total. In this case of 1 / 9, 1 is our numerator. The denominator (9) is located below the vinculum and represents the total number. In the example above 14 would be the denominator of cars. For our fraction: 1 is the numerator and 9 is the denoimator.\n\n### 2: Write out your equation of 1 / 9 times 47\n\nWhen solving for 1 / 9 of a number, students should write the equation as the whole number (47) times 1 / 9. The solution to our problem will always be smaller than 47 because we are going to end up with a fraction of 47.\n\n$$\\frac{ 1 }{ 9 } \\times 47$$\n\n### 3. Convert your whole number (47) into a fraction (47/1)\n\nTo convert any whole number into a fraction, add a 1 into the denominator. Now place 1 / 9 next to the new fraction. This gives us the equation below.\n\n$$\\frac{ 1 }{ 9 } \\times \\frac{ 47 }{1}$$\n\n### 4. Multiply your fractions together\n\nOnce we set our equations 1 / 9 and 47 / 1, we now need to multiple your values starting with the numerators. In this case, we will be multiplying 1 (the numerator of 1 / 9) and 47 (the numerator of our new fraction 47/1). If you need a refresher on multiplying fractions, please see our guide here!\n\n$$\\frac{ 1 }{ 9 } \\times \\frac{ 47 }{1} = \\frac{ 47 }{ 9 }$$\n\nOur new numerator is 47.\n\nThen we need to do the same for our denominators. In this equation, we multiply 9 (denominator of 1 / 9) and 1 (the denominator of our new fraction 47 / 1).\n\nOur new denominator is 9.\n\n### 5. Divide our new fraction (47 / 9)\n\nAfter solving for our new equation off 47 / 9, our last job is to simplify this problem using long division. For longer fractions, we recommend to all of our students to write this last part down and use left to right long division.\n\n$$\\frac{ 47 }{ 9 } = 5.22$$\n\nAnd so there you have it! Our solution is 5.22.\n\n#### Quick recap:\n\n• Turn 47 into a fraction: 47 / 1\n• Multiply 47 / 1 by our fraction, 1 / 9\n• Multiply the numerators and the denominators together\n• We get 47 / 9 from that\n• Perform a standard division: 47 divided by 9 = 5.22\n\n#### Additional way of calculating 1 / 9 of 47\n\nYou can also write our fraction, 1 / 9, as a decimal by simply dividing 1 by 9 which is 0.11. If you multiply 0.11 with 47 you will see that you will end up with the same answer as above. You may also find it useful to know that if you multiply 0.11 with 100 you get 11.0. Which means that our answer of 5.22 is 11.0 percent of 47." ]

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[ "# Writing clean long underscores [duplicate]\n\nPossible Duplicate:\nLong underscore in LaTeX\n\nI'm writing a document in which I encourage the reader to \"fill in the blanks\" in order to be actively engaged with the proof.\n\nIs there any way to write a clean, long underscore? Currently I'm using \\underline{\\hspace*{2cm}}, but it doesn't look so great...\n\nHere's a sample of my text:\n\n\\begin{thm}\n\n$A \\subset B$ if and only if $A \\cap B = A$.\n\n\\end{thm}\n\n\\begin{proof}\n\nAssume $A \\subset B$.\nWe want to show $A \\subset (A \\cap B)$ and \\underline{\\hspace*{2cm}}.\nThe first fact is true since: $A \\subset B \\Rightarrow$\nif $x \\in A$ then \\underline{\\hspace*{2cm}} $\\Rightarrow$\nif $x \\in A$ then $x \\in A \\textrm{ and } B$.\nThe second fact is true by \\underline{\\hspace*{2cm}}.\n\nConversly, assume \\underline{\\hspace*{2cm}}.\nBy the first property again, $B \\supset$ \\underline{\\hspace*{2cm}},\nso we have \\underline{\\hspace*{4cm}}.\n\n\\end{proof}\n\n• This question is also a duplicate of Long underscore in LaTeX. You can use the \\rule command instead to have more control over the look of the underscore. – Alan Munn Dec 2 '11 at 18:25" ]

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[ "### How much is 300 inches?\n\nConvert 300 inches. How far is 300 inches? What is 300 inches in other units? Convert to cm, km, in, ft, meters, mm, yards, and miles. To calculate, enter your desired inputs, then click calculate. Some units are rounded since conversions between metric and imperial can be messy.\n\n### Summary\n\nConvert 300 inches to cm, km, in, ft, meters, mm, yards, and miles.\n\n#### More Conversions below\n\n 300 inches to meters 300 inches to miles 300 inches to millimeters 300 inches to yards\n\n#### 300 inches to Other Units\n\n 300 inches equals 762 centimeters 300 inches equals 25 feet 300 inches equals 300 inches 300 inches equals 0.00762 kilometers\n 300 inches equals 7.62 meters 300 inches equals 0.004734848485 miles 300 inches equals 7620 millimeters 300 inches equals 8.333333333 yards" ]

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[ "# Activity B: Angle Bisectors\n\nAll three angle bisectors of a triangle will intersect at the same point - the incenter. Let the incenter be point I in the diagram.\n6) Do all of the angle bisectors meet at a point? (Drag the vertices of the triangle to create a variety of triangles to check if this is always true) 7) Will the incenter always be located inside of the triangle? Why or why not? 8) What can you conclude about the location of the incenter based on the type of triangle?

 9) The incenter is the center of the circle that is inscribed inside a triangle. What does it mean for a circle to be inscribed in a triangle? 10) How would you describe, in words, the length of the radius of the circle that is inscribed in a triangle? (Use point G to help with your description)" ]

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[ "", null, "", null, "### Home > INT2 > Chapter 11 > Lesson 11.2.2 > Problem11-72\n\n11-72.", null, "Prove that when two lines that are tangent to a circle intersect, the distances from the point of intersection to the points of tangency are equal. That is, in the diagram at right, when $\\overleftrightarrow { A D }$ is tangent to $⊙E$ at point $D$, and $\\overleftrightarrow { A F }$ is tangent to $⊙E$ at point $F$, prove that $AD = AF$. Use either a\nflowchart or a two-column proof.", null, "" ]

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SMAK/8hRgLL8S6SwvMcWDQzvascJkuopwm+szYqyA2SH3kRum89v6EE33NrjKLdwLy0Ffh2G4qUg32uVon3YtWxXrWXUEd8FCqftTH765n3cuqEC7zXUczvGyW8W5TzFrwvFmda1k/5wn0wEqelQJ7qWX/XlHC9Jr6z9hLrr0LRKws9tPhJS4FKutaTFjbUcSQcIhO48vcP7F9sZHWJhA58zshvpW/D9SoNNFAIMkRXQ27yHInWkL+ADa2LqTyGCXv+6ciz9GLs7aWfxLT3s4GIAxq8x5n2oALpQCB38X7PeXlw5bNM/2mmfdY59jz/38HjPr7BfFwVk4ejeXxG4NhHeN2XJJr/AOWJlfWOK/IO7D0v8fbv4z0Xnvlv3vNAfsf07+exh6ic+cR5Ae9jPVbYvijwbhDvMZv32jMmz0fy/FsK1P+TmZ9rCjz7VF7nm72ou7vElAfK6RGWq0/4tzL9PwJ1Au/04zH3QnDrLyRaCvkVvtvZRd7tRL7/13gOzv2l9OwGRPndXCBfuO8nipSFfbffKpBmBtNMLXKtk5gOsUTDlKYU/WmhZ2MIvbNCefqQ00BmaG3tE9Nozab2HCLoNY5G7Fp3owNp0T0wpgzFoFLYjB6Mnfn/VeYRDc6lEi0aM9GxEDZhwybcZxeoBfHbYMVT2ABZLX8bCqam/WlMPr4i+eF7Q4rkGaMbtuS76QqUWcJpxOud/HY69cfm91iS6IWedY38xgUsDuXxVd7+/VlvhrNsXmR5oSG+nedMi7EyJ/P4ZCoSqx2PyFjHE5Ry6ppb31c639P2tIirPCX4VxKtBgjMo/W1PZ/9Uzy2wrnODvRWYA6HCQEr3JbDigIWHIJGtyWxX0GPgA+U89Ysq3JRRyXGWrJZx1BA3vYyciiVsLWO8rgd03YG6vBRVODvcu6D7+MevosMFTYowntQcPw7Xt6+4xDnElrmyOsJLG8onU85dXIrJ1+2TXHzdQzzNTNG0Z1MRWwyvYAhq34sy+Ub/BbfiCnT8/jemjYy40PxHrTQQ+iqoFtoNK2PI9kQ7BtDtLDkf+6QiA806D8q4X7PsdFMDED5X83GaIFEa7uPpxxPUsAwv9O9cgZ+xgZ/R/4iNuA2ktN0yc++57pZz2BjEfIQuKMFisUjWCI7xcmDK+PZ+LrXQgO8k5Nmd8fC/j6f3ffQxE3qkw4QKkj8Jv7+kff6MJXDHzLNZVSQfNgpi4VKneuheJjPY8t5MvfPoQJkn/dwrx52eN/Dt0jYq1incc4H+X6XkbAv9JTmDsfrcEGJ5eBiJz4b0OwoE6FvN84zVgz2/UKp2I1ltAOf78tU9A/y6rDN77leHd6dym09CXGYo1TdSDKczfLYieV3GdOc79WhfRwyv5RpbZ14gG3M9Z4HzObrvJh81Xn58pXJcY6XZq8i3w6I+rSYNJ93PAgdou52xQAQ+kBgKt1icV6GIbRKFhS5DhqDtwcg/2igPsftMyVa/jXDjxgW5ZU8dnbAbbmazzWPv3B7TqIS00wLxMeOtH58wHrbtBf5X+TkwZW5bMh90niNx+fTMsJ8BLMc5aAv+CS9Bkv4PHNYlktIpo+wrp8ZOHcij83l/0nOsTbut+X8hkN+9nlej7G0xCGkE7l9Cb0IHSyTu0ggQqKPc69+m5ZoOTiGHoV5zO+kfqzLackHvM7n9g2S78I4WnpOKLXUq8OoEyfxnYEcd2G63aiItbKePM93i/7w7xm5m+lOdK5tn/XPVBiX8ZyX6alq4/UPCTwL7v8vL1+TuB+KcqhLwN77Nf6eUEKZTQ54C1EPz1JaUgw0oW/oRUlg2V5cJE2t89HH4T5q300DUPZoHBpp3TweOD6dpPftwHtKxlhLL3M7zl39TU8Bgqvwq45VWA7K6a6B5VoT2P9bx5rsSx3awfG2LA0cn0Kiv9Xb30yLKMuyWUhLb8uY+6Sc56ktMW9Qlmx/+gOB4w+R3DeR9fvdq0g8C3jfH5dxT6Q71lEGXqVC8MF+qstx5fG04wWqLaH+LCVxAkMdi1eoWL0WOOde/m7r7NveO+biLXrAzohRxEL5Wu7UK1/p2oyKwTpes4WK+ogSPJH+PBoHSnwMgULRL4Qeck03SnhseiXRzgbxMDZSxQjIRr+jEX8wcBxW0jkFnqm/Yee1XynhaG7sn0Fr3Y+E7o7xSNh+8IXesQdo2XzMs0pgOW1HC/8fZea/EjETbzl5b+jDdWwjG+dpQUAUgsf+GmhA4SlBlwC6CeBih2v1iAq+5yaSWafk+9r9et1CIqnzvrMsLbZVtCi/U+I94fL9AOsBvAD3U2Hqr9EdWQlH2u/rELVfx0PR+weQjLO08oHhzjUk5juxdci2aU1F6sPdVJifCRwL5etAyceCvOwd+yy/ZVjyCGJDtwCi8A8t0Hb+kt/w1x3FxSrcwEyJjw1SKCpiZbkNUKjRapJ8UE9fAGviSoeQYXku4wf+ai8UljQVgNmelfgTiSJJB7rsu6T8/stNaNW6VuC32OgsCxAXgv4w8c+1THc3G3jr3kMU9GllNN7AFWwwk16D9b2YhlJilCrrceiLhZ4sUDcLwbpGf+80pCdy/3SpzOp5SckPLQzFBXQ7+xMBJe0JiVzXeEfnUvF4usg9j3eIK81fBGIhIvxyqVwAq1uXMT/FWueZP8P8WgLzyxJW7OZMm6FX5EQqP4gHedF7t+uKKJZJpwxD9WFXfjdZJ13I6j/Cy9dYenf8fPllfadThw5mHZoRk2d8n2OoKEyi9wWWOUZ9wN3/fxLFZWj/uaLfCT2k9Q7nR+AT+v5s4NNO5QSp3sCPI4TFrNCVBAgGQTBnOhbs1AEue7dhKddDcDLFByL7vyw9o5mHsnFBfy2Gtu1GBeyjtDhmUukpB3EL8/y0DEJ3yyJbobIsFWioD2KjbUdVII5hCZ9tl148R2/ec7H3D+/Xj0jGu7Px372AEjhC8gFwv+bvoxL1Ce9A6/3+CtdlfP+PxRybwW/Px3HSc8hZG7/9s5xyK/ZuE166uHNQhhO8c690lA6LYwKeDHjIEIB7tqeYjGd5tku+L38W0+9PBXtujBJyNQkdVvr/UuGCAYKA1/kyMF5DxSAk9BcC+6C9fs2z8rDvssBHBFxVwPqp7qdnRV6OYkOOhV2WD3DZ9+WDfZtKSZKNACwjuPxulsi1HipTuG2voyJzjuOt+G82pMky84358Z+UvFswUaB+FPKgDFRZHk6yhJvddjesIrmfxkb9mQrlLdGH57CW4mkkzY+TBBbFXOMztEThfXrEsW7RdQOX/cR+IPRuWq7dfKcZEtmdjlLhA11hiB9AVx2i4D9EMjy1l+82UeQcxGu8QuPCkm1XgXwlWc7IF0ZOTAmktYGHs0jCwJtMj2NHSj641QW6l+5gvUM3GQJz0RXWQkLfSqlJsaEI/a8kR/+jQXAV+o7gEkRf4BdjyBxE9KCEg6T6E8v4cR0vPYOjBgJtzsddI4XXhk94FsgvJN//Xw5gZaCf7mj+XyDR+OjeAIQxu49lYPu+OyTvUrWKRZzClw4oA+scS7FURcK6SuGh2JPfQkbyoyKg/F1c5L2Ugg5aZPUSjhOwM9+JxA/Vs+WNbo6LJBri9ouYdLYb4SXvuawCcBjLaWUF6/JKWqpryzgHwai3OSQICxf90RjG+ZyTrt3xMoUwxClnW286vPplFVeLmwsQ+h+db+JNtmeH0ZvldtHVOJb8K3z+JOuntcqhPP1Qes7SZ2daRJ5ukXyA73S2Ux9QalL0Br2xkBBA9ZeYY0fzY/lpDJkDP6FLKjUAz3ujQ2YDjVX8qEfHNFZoQOACnik9I2t7a9kulfUnl7mOjXBvrldXgTKw0elLnEbYTuoyJuacTZ3ycz0WwLiYc6ZQibya/3eSfDQxJtV5lMdhrf+A+xE1vW8FnnEFSQllHJo2eRRJqU16Dvfzgbw9zXNs95Gr6CHP+3H7C95zXeeU38H94G0q1zho8Ej0CSo2/ph7G/W+eUybMc6rD1lHWdk65t7betcOKQhW6XhM8rP8uXBHDZxHb8iD/D2f+6Gc7FqgDOyshlYpvVYpSbGhCd0O8elNANzj1EIH0ipevJGU/Rx6K+okP3TMfS/Q2g8gma8ONKC9xfW0gEAMN/XhOi1lpE1Lz0AsDEeyE7Xc5+x/mL8TAoQKIjuJ2+5qfU84SpAfXTyWFu2+TkNvXaVv0Br7jSP4/6pDin3FUsfiDAUens73PUcKj2e3jf43aFmGukg+T6JEEOTtged6vsBztffxOftSJ9P0PgBwU3/CMyDWkZxPCNSHL3h1QBzP0XHSc6w3vAC7sx17rEi+YO3b2QWP8IwU6+GZS0+DW9b4P9/zBMV5by6nV+g6Cfe3KxQlo7f91a+wgt9awCoKWfbHSt9dmO8VrGUjdj01fFikGGJUS9I6hA3Kd6Uy0dYWi9lgurOR9QYns4FLBOoUvAovelb1+ZJ3PW5FTwkaW7g1f+aR80zWL/R7wmWJvkaMrf86FYGF9LZYPMWG9Bg2pldTYRlH5RPW3WtsNF1X6eUSng4XZT+Lv2OkbxMPZfme9yPBQIGzUd/HOXkBcZQy2uFJWuoXBAh1IrevlfA0txNIdgfwHSxwjkHhCc15kKLy9Eg/fw/38N1/gs/2WYcwf05FBvVkRyp9GP+Ncd8Y5vaW5GeNBG6gVwZu9XtZHkizN89JUZl9roR8WSt9Ar/FQ6lkH+5Y578LnIeI/RlUsnBea8z1URf+UKaCrFBUlNCFHzg+kMvYKMW5YGHJ3yzR0JvVXgPUHEhf7rKmdpUjH0PLuEbcilH93c8PMkFUMmaz+hLFAtbk2bJ+P7V1B5Y6ZrsupkxDQ4CaS3hmt6xPLZBuCQndXmszkqePZ+ideMuziibz3EMCxPQyFZ63A+ckaeH5i6y8SOsObtmjqBRkJD9TnY+H+Qyb0AK8xiub5hiLtNqpey4xoovqFF7ncIcMrKcDBHaHsy/pvOOQJY5vDv26OzvvAwqDndp2ZsxzQcnBzHbbsq5d6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null, "https://s3-us-west-2.amazonaws.com/c3po-media-dev/files/e889bf00-259f-11e9-ab6b-d7741872f579/Int2_final_11-72_original.png", null, "https://s3-us-west-2.amazonaws.com/c3po-media-dev/files/65ed0250-259f-11e9-ab6b-d7741872f579/ans-ch11-72_original.png", null ]

[ "", null, "", null, "", null, "", null, "## Entropy and expansion. (arXiv:1811.09560v1 [math.PR])\n\nShearer's inequality bounds the sum of joint entropies of random variables in terms of the total joint entropy. We give another lower bound for the same sum in terms of the individual entropies when the variables are functions of independent random seeds. The inequality involves a constant characterizing the expansion properties of the system. Our results generalize to entropy inequalities used in recent work in invariant settings, including the edge-vertex inequality for factor-of-IID processes, Bowen's entropy inequalities, and Bollob\\'as's entropy bounds in random regular graphs. The proof method yields inequalities for other measures of randomness, including covariance. As an application, we give upper bounds for independent sets in both finite and infinite graphs.查看全文\n\n## Solidot 文章翻译\n\n 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 Shearer's inequality bounds the sum of joint entropies of random variables in terms of the total joint entropy. We give another lower bound for the same sum in terms of the individual entropies when the variables are functions of independent random seeds. The inequality involves a constant characterizing the expansion properties of the system. Our results generalize to entropy inequalities used in recent work in invariant settings, including the edge-vertex inequality for factor-of-IID processes, Bowen's entropy inequalities, and Bollob\\'as's entropy bounds in random regular graphs. The proof method yields inequalities for other measures of randomness, including covariance. As an application, we give upper bounds for independent sets in both finite and infinite graphs.\n" ]

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[ "### Some code clean-up and preparation for the computation of topoindex within the HydroData class.\n\n`Topoindex will become optional if orography is present.`\nparent 7f3b7d2c\n ... @@ -772,7 +772,7 @@ SUBROUTINE correct_inflows(nbpt, nwbas, inflowmax, outflow_grid,& ... @@ -772,7 +772,7 @@ SUBROUTINE correct_inflows(nbpt, nwbas, inflowmax, outflow_grid,& INTEGER(i_std), DIMENSION(nbpt,nwbas,inflowmax), INTENT(inout) :: inflow_grid INTEGER(i_std), DIMENSION(nbpt,nwbas,inflowmax), INTENT(inout) :: inflow_grid ! LOCAL ! LOCAL INTEGER(i_std) :: ig, nbas, ib, og, ob, inf, found INTEGER(i_std) :: ig, nbas, ib, og, ob WRITE(numout,*) \"Checking if the HTUs are in the inflows of their outflow\" WRITE(numout,*) \"Checking if the HTUs are in the inflows of their outflow\" ... ...\n ... @@ -2866,7 +2866,6 @@ SUBROUTINE routing_reg_killbas(nbpt, ib, tokill, totakeover, nwbas, inflowmax, b ... @@ -2866,7 +2866,6 @@ SUBROUTINE routing_reg_killbas(nbpt, ib, tokill, totakeover, nwbas, inflowmax, b ! Update the information needed in the basin \"totakeover\" ! Update the information needed in the basin \"totakeover\" ! For the moment only area ! For the moment only area ! ! WRITE(numout, *) \"XXXXX Arguments : inflow_number = \", inflow_number(ib,1:10) ! ! basin_cg(ib, totakeover, 1) = (basin_cg(ib, totakeover, 1)*basin_area(ib, totakeover) & basin_cg(ib, totakeover, 1) = (basin_cg(ib, totakeover, 1)*basin_area(ib, totakeover) & & + basin_cg(ib, tokill, 1)*basin_area(ib, tokill))/(basin_area(ib, totakeover) + basin_area(ib, tokill)) & + basin_cg(ib, tokill, 1)*basin_area(ib, tokill))/(basin_area(ib, totakeover) + basin_area(ib, tokill)) ... ...\n ... @@ -93,9 +93,14 @@ class HydroGrid : ... @@ -93,9 +93,14 @@ class HydroGrid : class HydroData : class HydroData : def __init__(self, nf, box, index) : def __init__(self, nf, box, index) : istr, iend, jstr, jend = box[:] istr, iend, jstr, jend = box[:] # # Flow direction # self.trip=gather(nf.variables[\"trip\"][jstr:jend,istr:iend].astype(np.float32), index, 97) self.trip=gather(nf.variables[\"trip\"][jstr:jend,istr:iend].astype(np.float32), index, 97) self.tripdesc=nf.variables[\"trip\"].long_name self.tripdesc=nf.variables[\"trip\"].long_name # # # ID of basin # self.basins=gather(nf.variables[\"basins\"][jstr:jend,istr:iend], index, 999) self.basins=gather(nf.variables[\"basins\"][jstr:jend,istr:iend], index, 999) self.basinsdesc=nf.variables[\"basins\"].long_name self.basinsdesc=nf.variables[\"basins\"].long_name att = getattrcontaining(nf, \"basins\", \"max\") att = getattrcontaining(nf, \"basins\", \"max\") ... @@ -106,36 +111,33 @@ class HydroData : ... @@ -106,36 +111,33 @@ class HydroData : # This variable seems not to be used further # This variable seems not to be used further self.basinsmax = part.domainmax(np.ma.max(ma.masked_where(self.basins < 1.e10, self.basins))) self.basinsmax = part.domainmax(np.ma.max(ma.masked_where(self.basins < 1.e10, self.basins))) # # self.topoind=gather(nf.variables[\"topoind\"][jstr:jend,istr:iend].astype(np.float32), index, 10) # Distance to ocean self.topoinddesc=nf.variables[\"topoind\"].long_name att = getattrcontaining(nf, \"topoind\", \"min\") if len(att) > 0 : self.topoindmin=att else : INFO(\"We need to scan full file to find minimum topoind over domain\") self.topoindmin=np.min(np.where(nf.variables[\"topoind\"][:,:] < 1.e15)) # # self.topoindh=gather(nf.variables[\"topoind_h\"][jstr:jend,istr:iend].astype(np.float32), index, 10) self.topoindhdesc=nf.variables[\"topoind_h\"].long_name att = getattrcontaining(nf, \"topoind_h\", \"min\") if len(att) > 0 : self.topoindhmin=att else : INFO(\"We need to scan full file to find minimum topoind_h over domain\") self.topoindhmin=np.min(np.where(nf.variables[\"topoind_h\"][:,:] < 1.e15)) # # self.disto=gather(nf.variables[\"disto\"][jstr:jend,istr:iend].astype(np.float32), index, 0) self.disto=gather(nf.variables[\"disto\"][jstr:jend,istr:iend].astype(np.float32), index, 0) self.distodesc=nf.variables[\"disto\"].long_name self.distodesc=nf.variables[\"disto\"].long_name # # # Flow accumulation # self.fac=gather(nf.variables[\"fac\"][jstr:jend,istr:iend].astype(np.float32), index, 0) self.fac=gather(nf.variables[\"fac\"][jstr:jend,istr:iend].astype(np.float32), index, 0) self.facdesc=nf.variables[\"fac\"].long_name self.facdesc=nf.variables[\"fac\"].long_name # # # If Orography is present in the file then we can compute the topographic index. # Else the topographic index needs to be present in the file. # if \"orog\" in nf.variables.keys(): if \"orog\" in nf.variables.keys(): self.orog = gather(nf.variables[\"orog\"][jstr:jend,istr:iend].astype(np.float32), index, 0) self.orog = gather(nf.variables[\"orog\"][jstr:jend,istr:iend].astype(np.float32), index, 0) self.orogdesc=nf.variables[\"orog\"].long_name self.orogdesc=nf.variables[\"orog\"].long_name else: else: self.orog = gather(np.zeros((jend-jstr,iend-istr)).astype(np.float32), index) self.orog = gather(np.zeros((jend-jstr,iend-istr)).astype(np.float32), index) self.topoind=gather(nf.variables[\"topoind\"][jstr:jend,istr:iend].astype(np.float32), index, 10) self.topoinddesc=nf.variables[\"topoind\"].long_name att = getattrcontaining(nf, \"topoind\", \"min\") if len(att) > 0 : self.topoindmin=att else : INFO(\"We need to scan full file to find minimum topoind over domain\") self.topoindmin=np.min(np.where(nf.variables[\"topoind\"][:,:] < 1.e15)) # # # if \"floodplains\" in nf.variables.keys(): if \"floodplains\" in nf.variables.keys(): self.floodplains = gather(nf.variables[\"floodplains\"][jstr:jend,istr:iend].astype(np.float32), index, 0) self.floodplains = gather(nf.variables[\"floodplains\"][jstr:jend,istr:iend].astype(np.float32), index, 0) ... ...\n ... @@ -63,7 +63,10 @@ w = RPP.compweights(wfile, part, modelgrid, hydrogrid) ... @@ -63,7 +63,10 @@ w = RPP.compweights(wfile, part, modelgrid, hydrogrid) # # # # nbpt = len(w.index) nbpt = len(w.index) nbvmax = part.domainmax(max(w.hpts)) nbvmax = part.domainmax(w.maxhpts) # nbasmax = min(nbasmax,nbvmax) # INFO(\"nbpt : {0}\".format(nbpt)) INFO(\"nbpt : {0}\".format(nbpt)) INFO(\"nbvmax : {0}\".format(nbvmax)) INFO(\"nbvmax : {0}\".format(nbvmax)) INFO(\"nbasmax : {0}\".format(nbasmax)) INFO(\"nbasmax : {0}\".format(nbasmax)) ... ...\nMarkdown is supported\n0% or .\nYou are about to add 0 people to the discussion. Proceed with caution.\nFinish editing this message first!\nPlease register or to comment" ]

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[ "# Notes\n\n## Section 12: Evolution of Networks\n\n[Networks generated by] random replacements\n\nAs indicated in the note above, applying the second rule (T1, shown as (b) on page 511) at an appropriate sequence of positions can transform one planar network into any other with the same number of nodes. The pictures below show what happens if this rule is repeatedly applied at random positions in a network. Each time it is applied, the rule adds two edges to one face, and removes them from another. After many steps the pictures below show that faces with large numbers of edges appear. The average number of edges must always be 6 (see note above), but in a sufficiently large network the probability for a face to have n edges eventually approaches an equilibrium value of 8 (n - 2)(2n - 3)!! (3/8)n/n!. (For large n this is approximately λn with λ = 3/4; if 1- and 2-edged regions are allowed then λ = (3 + 3)/6 0.79.) There may be some easy way to derive such results, but so far it has only been done using fairly sophisticated techniques from quantum field theory developed in the late 1970s. The starting point is to look at a φ3 field theory with SU(n) internal symmetry and to note that in the limit n what dominates are Feynman diagrams that have the structure of planar trivalent networks (see page 1040). And it then turns out that in zero spacetime dimensions the complete path integral for the theory can be evaluated exactly—yielding in effect a generating function for the number of possible networks. Parametric differentiation (to yield n-point correlation functions) then gives results for n-sided regions. Another result that has been derived is that the average total number m[n] of edges of all faces around a given face with n edges is 7n + 3 + 9/(n + 1). Note that the networks obtained always have dimension 2 according to my definitions.", null, "From Stephen Wolfram: A New Kind of Science [citation]" ]

[ null, "https://www.wolframscience.com/nks/img/inline/page1039a.png", null ]

[ "", null, "Algebra\n\n# Algebra Common Misconceptions: Level 3 Challenges\n\n$\\large \\sqrt{-2}\\times\\sqrt{-3}=\\, ?$\n\nIn this problem, the square root is a function from the complex numbers to the complex numbers.\n\nIf $x$ and $y$ are non-zero numbers such that $x>y$, which of the following is always true?\n\n(A) $\\dfrac{1}{x}<\\dfrac{1}{y}$\n\n(B) $\\dfrac{x}{y}>1$\n\n(C) $|x|>|y|$\n\n(D) $\\dfrac{1}{xy^2}>\\dfrac{1}{x^2y}$\n\n(E) $\\dfrac{x}{y}>\\dfrac{y}{x}$\n\nCalvin has a collection of special weighted dice that all share special properties:\n\n• They're all 4 sided dice\n• Any one die has distinct positive integers on each of its faces\n• No pair of dice have all their numbers exactly the same\n• The probability of rolling number $x$ on any one of the dice is $\\frac {1}{x}$\n\nLet $a$ be the maximum number of dice in the collection and let $S$ be the sum of all the faces of all the dice in the maximum collection size.\n\nFind $a+S$.\n\nI claim that $1 < -1$ using the proof below but I was just told that I might have just committed a small mistake.\n\nA. $- ( i^4 - i^3 - i - 1)< 1 -i^2$\nB. $i^3 - i^4 + i + 1 < 1-i^2$\nC. $(i^3+i)(1-i) < (1-i)(1+i)$\nD. $i^3 + i < 1+i$\nE. $i^2(1+i) < 1+i$\nF. $i^2 < 1$\nG. $i^2 < i^4$\nH. $1 < i^2$\nI. $1 < -1$\n\nWhere did I go wrong? At which step(s) did I commit a fallacy?\n\nNote: $i = \\sqrt {-1}$.\n\nWhat is the wrong step in the following proof that $1 = -1$?\n\n1. Let $w$ be a complex number such that $(w + 1)^3 = (w - 1)^3$.\n\n2. Solving this equation gives $w = \\pm \\frac{i \\sqrt{3}}{3}$.\n\n3. Since $(w + 1)^3 = (w - 1)^3$ for our previously mentioned values of $w$, cube rooting both sides gives $w + 1 = w - 1$.\n\n4. Subtracting $w$ from both sides gives $1 = -1$.\n\n×" ]

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[ "# The Decibel\n\nThe decibel (dB) is a logarithmic unit used to express the ratio between two values of a physical quantity, most commonly sound pressure levels. The dB scale is a non-linear scale that compresses large ranges of values into a smaller, more manageable range. This makes it easier to compare values across a wide range of magnitudes.\n\nThe decibel scale is based on the logarithm of the ratio between two values. The formula for calculating the decibel level of a sound is:\n\ndB = 20 log10 (P/P0)\n\nwhere dB is the decibel level, P is the sound pressure level being measured, and P0 is the reference sound pressure level, which is typically set at 20 micropascals (μPa) for air.\n\nThe decibel scale is a relative scale, which means that it does not have an absolute zero point. Instead, it is based on the difference between two values, with one value serving as a reference point. For sound, the reference point is usually set at the threshold of hearing, which is the minimum sound pressure level that can be detected by the human ear. This reference point is given a value of 0 dB.\n\nThe decibel scale is logarithmic, which means that a change in the decibel level by a certain amount corresponds to a change in the sound pressure level by a certain ratio. For example, a change of 10 dB corresponds to a change in the sound pressure level by a factor of 10. Therefore, a sound that is 10 dB louder than another sound has 10 times the sound pressure level.\n\nThe decibel scale is used to express a wide range of sound pressure levels, from the faintest sound that can be heard by the human ear to the loudest sound that can be produced. The threshold of hearing is set at 0 dB, while the threshold of pain is around 140 dB. Sound levels between 0 dB and 140 dB are classified as varying degrees of loudness, with sounds above 85 dB considered potentially harmful to human hearing.\n\nThe decibel scale is also used to express other physical quantities besides sound pressure levels, such as power levels, voltage levels, and radiation levels. In these cases, the reference point and the formula used to calculate the decibel level may differ, but the underlying principle is the same: to express a ratio between two values in a logarithmic scale.\n\nThe decibel scale is a valuable tool for measuring and comparing sound pressure levels, as it allows for a wide range of values to be expressed in a manageable and meaningful way. It is used in a variety of fields, from audio engineering and acoustics to telecommunications and environmental noise monitoring.\n\nHowever, it is important to remember that the decibel scale is a relative scale and does not provide information on the actual physical properties of the sound being measured. In addition, the decibel scale does not take into account other important factors such as the frequency content of the sound, which can have a significant impact on how it is perceived by the human ear.\n\nIn conclusion, the decibel is a logarithmic unit used to express the ratio between two values of a physical quantity, most commonly sound pressure levels. It is a valuable tool for measuring and comparing sound pressure levels, but it is important to use it in conjunction with other measures and considerations to fully understand the properties of the sound being measured." ]

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[ "# What is the Greatest Common Factor of 108 and 118?\n\nGreatest common factor (GCF) of 108 and 118 is 2.\n\nGCF(108,118) = 2\n\nWe will now calculate the prime factors of 108 and 118, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 108 and 118.\n\nGCF Calculator and\nand\n\n## How to find the GCF of 108 and 118?\n\nWe will first find the prime factorization of 108 and 118. After we will calculate the factors of 108 and 118 and find the biggest common factor number .\n\n### Step-1: Prime Factorization of 108\n\nPrime factors of 108 are 2, 3. Prime factorization of 108 in exponential form is:\n\n108 = 22 × 33\n\n### Step-2: Prime Factorization of 118\n\nPrime factors of 118 are 2, 59. Prime factorization of 118 in exponential form is:\n\n118 = 21 × 591\n\n### Step-3: Factors of 108\n\nList of positive integer factors of 108 that divides 108 without a remainder.\n\n1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54\n\n### Step-4: Factors of 118\n\nList of positive integer factors of 118 that divides 108 without a remainder.\n\n1, 2, 59\n\n#### Final Step: Biggest Common Factor Number\n\nWe found the factors and prime factorization of 108 and 118. The biggest common factor number is the GCF number.\nSo the greatest common factor 108 and 118 is 2.\n\nAlso check out the Least Common Multiple of 108 and 118" ]

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[ "# work hours calculator Working", null, "## Working hours calculator for a year\n\nWork hour calculator, tool for calculating work hours over a year, excluding holidays and public holidays Calculation of hours worked over a period of 12 months Consider a worker who work 35 hours per week, 4 vacation weeks and 5 public holidays (for a total of 5\nHours calculator\nWith the hours calculator you can track your time (e.g. worktime). The hours calculator calculates the total of your working hours. If you enter your hourly rate to the timesheet the hours calculator also calculates your total salary. The hours calculator is the perfect\n\n## ‎Calculate Hours Worked on the App Store\n\n‎Calculate Hours Worked – Easy and Quick! Enter: Log-in time Log-out time And get the Total of hours worked. Enter the hourly pay rate to see the total amount due. A hassle-free calculator with no learning curve… Email or Download the results for future reference. ADVANCED FEATURES: In the Tota…\nFree Online Timsheet Calculator\nThe work hours calculator partially complies with California Overtime Law. The timesheet calculator is equipped with daily overtime functionality. This allows you to account for daily overtime hours incurred in excess of 8 hours. However, the timesheet calculator does\nOvertime Calculator\nOur overtime calculator is the perfect tool to help you see how much money you will earn in exchange for those extra hours at work. Fill in the information about how much your hourly rate is and the calculator will do all the rest. It will show you the rate of overtime\n\nThis calculator will add up hours and minutes for any number of time blocks, and convert minutes to decimal numbers at the same time. You can also set the calculator to auto-tab to the next field upon entering a customizable number of digits. Plus, when auto-tab\n\n## How to calculate number of work hours in a year? …\n\n· When calculating full-time hours, it is important to subtract these hours from the total work hours to figure out how many hours an employee will be working. For example, if a person works 8 hours a day, but gets 8 holidays a year and 12 vacation days, you would subtract 160 hours from the total 2,080 work hours per year to learn that the employee works 1,920 hours per year.\nWork Hours Savings Calculator\n\n## Gross Pay Calculator\n\nCalculator Use Calculate gross pay, before taxes, based on hours worked and rate of pay per hour including overtime. To enter your time card times for a payroll related calculation use this time card calculator. Gross Pay or Salary: Gross pay is the\nwork stuff\nThe calculator on this page will not calculate minimum off-the-job training hours for Apprentices working less than 30 hours per week. Maximum Working Hours All employees (including Apprentices) working in the UK are subject to laws regarding the maximum hours that can be worked per week.\nOvertime Calculator\n· This overtime calculator is a tool that finds out how much you will earn if you have to stay longer at work. All you have to do is provide some information about your hourly wages, and it will calculate what is the total pay you will receive this month. Keep reading to\n\n## Power Calculator, Calculate Work, Time.\n\nPower with Work Calculator English Español Power is the rate at which work is done. Here we can calculate Power, Work, Time Power with Work Calculation I want to calculate Work(W) N-m Time(T) S Power(P) W Calculator Formula Power is the rate at Here\n\n## Business Days Calculator – Count Workdays\n\nDate Calculator – Add or subtract days, months, years Birthday Calculator – Find when you are 1 billion seconds old Week Number Calculator – Find the week number for any date Related Links Date/calendar related services – Overview Calendar Generator\n\n## Free Timecard Calculator with Breaks, Payroll Hours & …\n\nFree Online Timecard Calculator with Breaks and Overtime Pay Rate Enter working hours for each day, optionally add breaks and working hours will be calculated automatically. If you want to calculate total gross pay, enter hourly pay rate and choose overtime rate in format “1.5” for 150% overtime rate.\nWork Hours Per Month for 2021\nWork Hours Per Month for 2021 Select a year and the calendar for that year is displayed along with the total working hours for each month (based on 8 hours each Monday-Friday). Hawaii State holidays are optionally indicated but not removed from the calculated hours.\nEmployee Timesheets Excel Template\nDownload a simple and effective Timesheet template or Time Card template. https://indzara.com/2018/09/timesheet-template-excel/ In this video, I will present" ]

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[ "Home | Menu | Get Involved | Contact webmaster", null, "", null, "", null, "", null, "", null, "# Number 207921981\n\ntwo hundred seven million nine hundred twenty one thousand nine hundred eighty one\n\n### Properties of the number 207921981\n\n Factorization 3 * 37 * 1873171 Divisors 1, 3, 37, 111, 1873171, 5619513, 69307327, 207921981 Count of divisors 8 Sum of divisors 284722144 Previous integer 207921980 Next integer 207921982 Is prime? NO Previous prime 207921949 Next prime 207922003 Is a Fibonacci number? NO Is a Bell number? NO Is a Catalan number? NO Is a factorial? NO Is a regular number? NO Is a perfect number? NO Polygonal number (s < 11)? NO Binary 1100011001001010001100111101 Octal 1431121475 Duodecimal 59771279 Hexadecimal c64a33d Square 43231550182964361 Square root 14419.500026006 Natural logarithm 19.152673475955 Decimal logarithm 8.3179004043021 Sine 0.3305027231673 Cosine 0.9438050381191 Tangent 0.35018113892033\nNumber 207921981 is pronounced two hundred seven million nine hundred twenty one thousand nine hundred eighty one. Number 207921981 is a composite number. Factors of 207921981 are 3 * 37 * 1873171. Number 207921981 has 8 divisors: 1, 3, 37, 111, 1873171, 5619513, 69307327, 207921981. Sum of the divisors is 284722144. Number 207921981 is not a Fibonacci number. It is not a Bell number. Number 207921981 is not a Catalan number. Number 207921981 is not a regular number (Hamming number). It is a not factorial of any number. Number 207921981 is a deficient number and therefore is not a perfect number. Binary numeral for number 207921981 is 1100011001001010001100111101. Octal numeral is 1431121475. Duodecimal value is 59771279. Hexadecimal representation is c64a33d. Square of the number 207921981 is 43231550182964361. Square root of the number 207921981 is 14419.500026006. Natural logarithm of 207921981 is 19.152673475955 Decimal logarithm of the number 207921981 is 8.3179004043021 Sine of 207921981 is 0.3305027231673. Cosine of the number 207921981 is 0.9438050381191. Tangent of the number 207921981 is 0.35018113892033" ]

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[ "# Number 23767415318\n\n### Properties of number 23767415318\n\nCross Sum:\nFactorization:\nDivisors:\nCount of divisors:\nSum of divisors:\nPrime number?\nNo\nFibonacci number?\nNo\nBell Number?\nNo\nCatalan Number?\nNo\nBase 3 (Ternary):\nBase 4 (Quaternary):\nBase 5 (Quintal):\nBase 8 (Octal):\nBase 16 (Hexadecimal):\n588a5fa16\nBase 32:\nm4abugm\nsin(23767415318)\n0.6948675726064\ncos(23767415318)\n-0.71913771736719\ntan(23767415318)\n-0.96625104736595\nln(23767415318)\n23.891581375259\nlg(23767415318)\n10.375981955217\nsqrt(23767415318)\n154166.84247269\nSquare(23767415318)\n5.648900308983E+20\n\n### Number Look Up\n\nLook Up\n\n23767415318 (twenty-three billion seven hundred sixty-seven million four hundred fifteen thousand three hundred eighteen) is a unique figure. The cross sum of 23767415318 is 47. If you factorisate the figure 23767415318 you will get these result 2 * 17 * 699041627. The number 23767415318 has 8 divisors ( 1, 2, 17, 34, 699041627, 1398083254, 11883707659, 23767415318 ) whith a sum of 37748247912. The number 23767415318 is not a prime number. The number 23767415318 is not a fibonacci number. 23767415318 is not a Bell Number. The figure 23767415318 is not a Catalan Number. The convertion of 23767415318 to base 2 (Binary) is 10110001000101001011111101000010110. The convertion of 23767415318 to base 3 (Ternary) is 2021100101120210111102. The convertion of 23767415318 to base 4 (Quaternary) is 112020221133220112. The convertion of 23767415318 to base 5 (Quintal) is 342133424242233. The convertion of 23767415318 to base 8 (Octal) is 261051375026. The convertion of 23767415318 to base 16 (Hexadecimal) is 588a5fa16. The convertion of 23767415318 to base 32 is m4abugm. The sine of the figure 23767415318 is 0.6948675726064. The cosine of the number 23767415318 is -0.71913771736719. The tangent of the figure 23767415318 is -0.96625104736595. The square root of 23767415318 is 154166.84247269.\nIf you square 23767415318 you will get the following result 5.648900308983E+20. The natural logarithm of 23767415318 is 23.891581375259 and the decimal logarithm is 10.375981955217. that 23767415318 is special figure!" ]

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[ "1. Home\n2. Training Library\n3. Machine Learning\n4. Machine Learning Courses\n5. Module 2 - Maths for Machine Learning - Part Two\n\n# Module 2 - Maths for Machine Learning - Part Two\n\n## Contents\n\n###### Maths for Machine Learning\n5\nMatrices\n12m 22s\nLinear Regression in Multiple Dimensions\nOverview\nDifficulty\nBeginner\nDuration\n1h 32m\nStudents\n681\nRatings\n3.5/5\nDescription\n\nTo design effective machine learning, you’ll need a firm grasp of the mathematics that support it. This course is part two of the module on maths for machine learning. It focuses on how to use linear regression in multiple dimensions, interpret data structures from the geometrical perspective of linear regression, and discuss how you can use vector subtraction. We’ll finish the course off by discussing how you can use visualized vectors to solve problems in machine learning, and how you can use matrices and multidimensional linear regression.\n\nPart one of this module can be found here and provides an intro to the mathematics of machine learning, and then explores common functions and useful algebra for machine learning, the quadratic model, logarithms and exponents, linear regression, calculus, and notation.\n\nTranscript\n\n### Lectures", null, "" ]

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[ "# A contribution to the theory of acoustic radiation\n\nC.J. Bouwkamp\n\nResearch output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review\n\n## Abstract\n\nThe field of radiation produced by a harmonically oscillating membrane with arbitrary amplitude distribution in a closely fitting aperture of an infinite rigid plane is studied. The analysis does not take into account the viscosity of the medium nor any other deviation from its \"ideal\" behavior.Numerical calculations are not given. Attention is paid mainly to the mathematical formalism. In section 1 the problem is mathematically stated by means of the velocity potential in the form of a boundary value problem in connection with the wave equation. A new argument is given as to why the time factor exp (-iwt) is preferred in theoretical considerations. Section 2 contains a brief sketch of the derivation of the now already classical Rayleigh formula, together with some critical remarks. Section 3 is devoted to energy considerations. The definitions of acoustic impedance and radiation characteristic are given. In addition formulae are derived by means of which they can be computed in the case of any prescribed source distribution. In section 4 the general formulae are applied to a circular membrane, oscillating with azimuthal and radial nodal lines. In section 5 King's theory of the circular disc oscillating with uniform amplitude is very much extended. The theory can be developed in terms of cylindrical wave functions. It is possible to express the velocity potential as a definite integral involving Bessel functions. It is shown that the reactive part of the acoustic impedance of any harmonically vibrating membrane of whatever amplitude distribution is always negative. This part can be calculated by integrating the radiation pattem over complex space directions. Section 6 shows expansions in spherical wave functions, applied to the radiation field of a membrane oscillating with nodal lines. King's statement that the theory of Backhaus regarding certain expansions in spherical coordinates does not hold is shown to be erroneous. For the sake of completeness the theory of section 6 is worked out in detail in the case of the Rayleigh plate. This is to be found in section 7. To preserve the reader from many tedious operations the majority of the necessary mathematical calculations are given in a separate mathematical appendix.\nOriginal language English Selected Papers on Scalar Wave Diffraction K.E. Oughstun Bellingham WA, USA SPIE 41-67 Published - 1992\n\n### Publication series\n\nName SPIE Milestone Series 51\n\n## Fingerprint\n\nDive into the research topics of 'A contribution to the theory of acoustic radiation'. Together they form a unique fingerprint." ]

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[ "Community Profile", null, "# L'O.G.\n\nAktiv seit 2022\n\n#### Statistiken\n\n•", null, "Abzeichen anzeigen\n\n#### Content Feed\n\nAnzeigen nach\n\nFrage\n\nHow to do this unusual Fourier transform?\nI am trying to compute a sine transform: I'm not sure about the non-standard bound of the integral (why it's not infinity...\n\n29 Tage vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nSolving linear systems in Matlab\nHow do I solve for x in u = A(x+b)? A is a matrix, and the other terms are vectors. Isn't it something like x = A\\u - b ? I'm no...\n\n30 Tage vor | 2 Antworten | 0\n\n### 2\n\nAntworten\n\nFrage\n\nRunge-Kutta with a function that changes at each time step\nI previously asked a question about solving an equation dx/dt = u(x,t) where u(x,t) is a velocity. I want to solve for the posit...\n\netwa ein Monat vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nUsing Runge-Kutta in Matlab\nI am trying to solve an equation dx/dt = f(x,t) where f(x,t) is a velocity. I want to solve for the positions x to obtain the tr...\n\netwa ein Monat vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nIntegrating a constant?\nThis is more of a physics question than a Matlab question, but given an instantaneous velocity vx and a time increment dt, how d...\n\netwa 2 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nNumerical integral where the bounds change with each evaluation\nI'm trying to take the following integral: I tried this symbolically, but I think that was throwing me off. I am attachin...\n\n4 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nHow to take an integral symbolically and then convert it to type double?\nHow do I take the following integral symbolically? And convert it to double? I have a 1000 x 1 numeric vector of type double for...\n\n4 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nInverse of a matrix\nI want to solve the following for X2: A = B(X1+X2) where B is a matrix, and A, X1, and X2 are vectors. I can't divide by a matri...\n\n4 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nIntegration when some of the values change over time\nI have a function of the form where is the position of the k-th object and is the corresponding force. The force has a functio...\n\n4 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nHow can I detect the object in this noisy image?\nI'm trying to process images like the attached. In this case, there should be an object near the center of the image around test...\n\n5 Monate vor | 2 Antworten | 0\n\n### 2\n\nAntworten\n\nFrage\n\nCell arrays with a vector within a cell within a cell\nI have a cell array where each element consists of a 1 x 1 cell containing a vector of type double, i.e., C{1,1} contains a vect...\n\n5 Monate vor | 3 Antworten | 0\n\n### 3\n\nAntworten\n\nFrage\n\nHow do you convert the cell within a cell to a vector?\nI have a cell of cells. The inner cell is a 1 x 1 and contains a vector. The vector in each inner cell might be of different len...\n\n5 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nHow to output a cell array as a table where the arrays contain vectors of different length?\nI have a cell array C that is 3 x 10, with each element containing a vector of numbers of type double. Each vector is of a diffe...\n\n5 Monate vor | 2 Antworten | 0\n\n### 2\n\nAntworten\n\nFrage\n\nWorking with cell arrays\nI would like to separate columns in an array based on the unique values of the first column. I think the way to do this is a cel...\n\n5 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nHow do I read each frame of a video?\n\n5 Monate vor | 2 Antworten | 0\n\n### 2\n\nAntworten\n\nFrage\n\nFinding first value in an array equal to each number in a vector\nI can find the first value in test_array that is equal to 2 using the following: find(test_array==2, 1, 'first') But how d...\n\n5 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nWhat is the previous syntax for this function?\nI can combine strings using something like str = append(\"Hello\",\"world\") But I have access only to Matlab 2018a. The append fu...\n\n5 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nHow to remove repeating entries from a vector?\nHow do you remove repeating entries in a vector? For example: A = [1 1 1 0 0 1 1 1 1 0 0 0 0 0] should return B = [ 1 0 1 0]....\n\n5 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nVectorization problem for grouping entries in an array\nThe data below are grouped into three different subgroups based on the value of B(:,3). If, however, B(:,2) <= 1, how do I indic...\n\n5 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nHow do you reshape an array to preserve the order in each row of the original array?\nHow do you reshape an array into a 1-dim column such that the first row of the original array is the first set of numbers in the...\n\n6 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nHow do you set entries in a matrix for odd rows with odd columns to zero?\nI want to set A(i,j) = 0 if both i and j are odd. Is this possible to do vectorially?\n\n7 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nHow do you make the diagonal and certain off-diagonal elements of a matrix zero?\nI have a square matrix and would like to make the diagonal elements zero, as well as select elements that are off-diagonal. For ...\n\n7 Monate vor | 2 Antworten | 0\n\n### 2\n\nAntworten\n\nFrage\n\nx values when taking a numerical derivative\nI want to calculate the first derivative f(x) = dy/dx for data that is irregularly spaced in x. I think (correct me if I'm wrong...\n\n8 Monate vor | 5 Antworten | 0\n\n### 5\n\nAntworten\n\nFrage\n\nChanging the position of a plot\nHow do you move everything in a figure (plot, axes, axis labels) up while preserving the aspect ratio of the plot? It seems I ca...\n\n8 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nHow can you shift the position of x axis labels?\nI can generate a scatter plot with the x axis labels of type categorical or string. When I rotate them slightly, I would like th...\n\n8 Monate vor | 1 Antwort | 1\n\n### 1\n\nAntwort\n\nFrage\n\nHow do I remove the tick marks on a bar plot at the top and the right?\nI can do this by box off but that also removes the lines. How can I keep the lines on the top and the right of the plot, but jus...\n\n8 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nCentering labels in a bar plot\nHow do I center a string under each bar at in a bar plot? Something like the following is the best I can do, but it's a lot of t...\n\n8 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nHow to sample from a distribution?\nHow do you use randsample (or maybe something else?) to sample from a distribution? Can you define a non-standard distribution a...\n\n8 Monate vor | 1 Antwort | 0\n\n### 1\n\nAntwort\n\nFrage\n\nLog-log plot with error band that has negative numbers\nHow do I make an error band? I am attaching some sample data. The fill function generates negative numbers, so that when I try e...\n\n8 Monate vor | 1 Antwort | 0\n\nAntwort\n\nFrage" ]

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[ "# Convert 3.984 CM to Inches\n\n## How many inches is in a centimeter?\n\nDo you wish to convert 3.984 cm to the equivalent of inches? first you need to know how many inches 1 cm is equal to.\n\nThis is how I will be specific: one cm equals 0.3937 inches.\n\n## What is centimeter?\n\nThe centimeter unit is a base unit of length.\nIt equals to 10 millimeters.\nThis unit is used in CGS system, maps, home repaire and all areas in our life.\nA single centimeter is approximately equivalent to 39.37 inches.\n\n## What is Inch?\n\nThe inch is a unit of length in the UK and the US customary systems of measurement. An inch is equal to 1/12 of a foot or 1/36 yard.\n\n## How do I convert 1 cm to inches?\n\nFor 1cm to inches conversion, multiply 1cm using a conversion factor 0.3937.\n\nThis makes it easier for you to calculate 3.984 cm to inches.\n\nAlso, 1 cm into inches = 1 cm x 0.3937 = 0.3937 inches, precisely.\n\n• What is one centimeter to inches?\n• What is the cm to inch conversion?\n• How many inches equals 1 cm?\n• What is 1 cm equivalent to in inches?\n\n### How to convert 3.984 cm to inches?\n\nYou have a good understanding of cm to inches from the above.\n\nThis is the formula:\n\nValue in inches = value in cm × 0.3937\n\nSo, 3.984 cm to inches = 3.984 cm × 0.3937 = 1.5685008 inches\n\nThis formula will allow you to answer the following questions:\n\n• What is 3.984 cm equal to in inches?\n• How can you convert cm into inches?\n• How to change cm to inches?\n• How do you measure cm to inches?\n• How tall are 3.984 cm to inches?\n\n cm inches 3.784 cm 1.4897608 inches 3.809 cm 1.4996033 inches 3.834 cm 1.5094458 inches 3.859 cm 1.5192883 inches 3.884 cm 1.5291308 inches 3.909 cm 1.5389733 inches 3.934 cm 1.5488158 inches 3.959 cm 1.5586583 inches 3.984 cm 1.5685008 inches 4.009 cm 1.5783433 inches 4.034 cm 1.5881858 inches 4.059 cm 1.5980283 inches 4.084 cm 1.6078708 inches 4.109 cm 1.6177133 inches 4.134 cm 1.6275558 inches 4.159 cm 1.6373983 inches" ]

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[ "315 plus 39 percent\n\nHere we will teach you how to calculate three hundred fifteen plus thirty-nine percent (315 plus 39 percent) using two different methods. We call these methods the number method and the decimal method.\n\nWe start by showing you the illustration below so you can see what 315 + 39% looks like, visualize what we are calculating, and see what 315 plus 39 percent means.", null, "The dark blue in the illustration is 315, the light blue is 39% of 315, and the sum of the dark blue and the light blue is 315 plus 39 percent.\n\nCalculate 315 plus 39 percent using the number method\nFor many people, this method may be the most obvious method of calculating 315 plus 39%, as it entails calculating 39% of 315 and then adding that result to 315. Here is the formula, the math, and the answer.\n\n((Number × Percent/100)) + Number\n((315 × 39/100)) + 315\n122.85 + 315\n= 437.85\n\nRemember, the answer in green above is the sum of the dark blue plus the light blue in our illustration.\n\nCalculate 315 plus 39 percent using the decimal method\nHere you convert 39% to a decimal plus 1 and then multiply it by 315. We think this is the fastest way to calculate 39 percent plus 315. Once again, here is the formula, the math, and the answer:\n\n(1 + (Percent/100)) × Number\n(1 + (39/100)) × 315\n1.39 × 315\n= 437.85\n\nNumber Plus Percent\nGo here if you need to calculate any other number plus any other percent.\n\n316 plus 39 percent\nHere is the next percent tutorial on our list that may be of interest." ]

[ null, "https://percent.info/images/plus/plus-39-percent.png", null ]

[ "# Finding the nth machine encountered on the journey\n\nRecently I came across this problem in the IARCS server,here is an little excerpt from it,\n\nA well-known bandit who used to haunt the forests around Siruseri was eliminated by the policemen a few months ago. There are several stories about a valuable treasure that he is alleged to have buried somewhere in the forest.\n\nThe deceased bandit had several hideouts and the police found a lot of things in these hideouts --- a number of guns, ammunition, knives, ... Interestingly, in every hideout there was a strange looking machine. This machine looked a bit like the weighing machine that is found in Indian railway stations where you insert a coin and get a card with your weight printed on it. The police had no idea what these machines were meant for and since they were heavy and in the middle of the forest they just left them there.\n\nOnly one man knew that the clue to the buried treasure was in these innocuous looking machines and that was Muttal. Muttal used to be part of the dacoit's band of robbers but was thrown out for being too dumb.\n\nHere is how the treasure was to be found. One had to insert a 1 rupee coin into one of these machines. This machine would then put out a token and a card on which was printed the name of the machine to be visited next. The token was then to be inserted into the machine whose name was printed on the card. The new machine would, in turn, produce another token and another card with a new destination printed on it, and so on.\n\nIf you started with by putting a 1 rupee coin in the correct machine place and followed the sequence of machines indicated by the cards, inserting each token produced by one machine into the next one, eventually one of these machines would put out a map to the treasure. Unfortunately, though, Muttal did not know which machine one should begin with.\n\nUnknown to Muttal, the bandit had played one last joke on the world. Knowing his end was near, he had reprogrammed these machines. There was no longer any map. All that you got for inserting a token in any machine was another token and a card leading you to the next machine. So poor Muttal is going to spend the rest of his life inserting tokens into machines and walking from one machine to another.\n\nYou are given M machines that generate and respond to T different kinds of tokens. We regard the 1 rupee coin also as one of the T types of tokens. For each machine m and each token t you are told what happens when t is inserted into m: that is, which token is produced by m and what the next destination printed on the card is.\n\nYour task is the following. Given the identity of the machine where Muttal starts his search and an integer N, identify the Nth machine that Muttal will visit. Muttal always begins his search by inserting a 1 rupee coin into the first machine.\n\nFor example suppose there are three machines and two kinds of tokens and the description of the machines is as follows:", null, "We take T1 to represent the one rupee coin. If Muttal starts at machine M1 then the sequence of machines he visits is M1, M2, M3, M1, M2, M3, ... Thus, the fourth machine he visits is M1, the fifth machine he visits is M2 and so on.\n\nSo I have worked a little on the code , but I get Time limit exceeded for some last output , I was thinking of an modulo thing , but not sure of it, here is what I am working on,\n\n#include <iostream>\n#include <vector>\n\nint main(){\nint machines , tokens , start , end;\nstd::cin >> machines >> tokens >> start >> end;\nstart--;end--;\nstd::vector<std::vector<int> >tokenTable(machines,std::vector<int>(tokens));\nstd::vector<std::vector<int> >machTable(machines,std::vector<int>(tokens));\n//std::vector<std::vector<int> >visited(machines,std::vector<int>(tokens));\nstd::vector<int>visitedMach;\nfor(int i=0;i<machines;i++){\nfor(int j=0;j<tokens;j++){\nint tok , mach;\nstd::cin >> tok >> mach;\ntok--;mach--;\ntokenTable[i][j] = tok;\nmachTable[i][j] = mach;\n}\n}\n\nint moves =0 ,token = 0;\n\nwhile(moves < end){\n/*if(visited[start][token]){\nint remaining = moves - visited[start][token]+1;\nint modFac = (end-visited[start][token])%remaining;\nif(modFac == 0){\nmodFac = remaining;\n}\nmodFac = modFac + visited[start][token];\n//std::cout << visited[start][token] << ' ' << moves <<' ' <<modFac<<std::endl;\nstd::cout <<visitedMach[modFac]+1<< std::endl;\nreturn 0;\n}\nvisited[start][token] = moves;\nvisitedMach.push_back(start);*/\nint newTok = tokenTable[start][token];\nint newStart = machTable[start][token];\ntoken = newTok;\nstart = newStart;\nmoves++;\n}\nstd::cout << start+1 << std::endl;\nreturn 0;\n}\n\n\nThe code in the comments is what I was thinking of doing but not sure of it, do you guys have some better approach for this problem?\n\nWhat we have here is a two-dimensional map, where each pair maps to a new pair.\n\nWe could pre-allocate a single contiguous vector like this:\n\nstd::vector<size_t> treasureMap;\ntreasureMap.resize(machines * tokens);\n\n\nThen, taking the example from the question, item 0, i.e. machine M1, token T1 would point to index 3 (machine M2, token T2). The whole vector from the example would look like this:\n\n[3, 2, 4, 5, 0, 1]\n\nOr, in code, when we read tokens and machines\n\ntreasureMap[i * tokens + j] = mach * tokens + tok\n\n\nSo, we have an optimized allocation, and optimized walkthrough when we iterate from the starting point.\n\nsize_t currentPos = start;\nfor (size_t i = 0; i < moves; ++i)\ncurrentPos = treasureMap[currentPos];\n\n\nI'm not sure if it will give you enough speed to pass the challenge though. If not, at least the code looks nicer.\n\n• I highly doubt on it , partly cause havent used size_t and manual memory allocation earlier and partly because of the number of inputs which is about 1000000000 and that thing is not small , thanks for answering – hellozee Oct 29 '16 at 17:07\n• As per the answer below: we should add loop detection into the algorithm. One way is to keep a set of all visited locations; once we detect that we're in a loop, we can short-circuit the whole evaluation. – RomanK Oct 29 '16 at 21:15\n\nSo the first think to define is the state of Muttal on the route, which is a pair of the current token and machine, which incidentally are two unsigned numbers\n\nusing machineMap = std::vector<std::pair<int, int>>;\n\n\nNow for every machine we would create a mapping, that gives us the next token and the next machine.\n\nstd::vector<machineMap> mapping(numMachines, machineMap(numTokens));\nfor (subMapping : mapping) {\nfor (map : subMapping) {\nstd::cin >> map.first >> map.second;\n}\n}\n\n\nAlso you should utilize a for loop whenever you know the number of steps instead of a while loop.\n\nauto currentPos = std::make_pair(0, firstMachine);\nfor (size_t step = 0; step < numSteps; ++step) {\ncurrentPos = mapping[currentPos.second][currentPos.first];\n}\n\n\nIn total that would give us\n\n#include <iostream>\n#include <utility>\n#include <vector>\n\nint main() {\nusing machineMap = std::vector<std::pair<int, int>>;\nsize_t numMachines , numTokens , firstMachine , numSteps;\nstd::cin >> numMachines >> numTokens >> firstMachine >> numSteps;\nfirstMachine--;\nnumSteps--;\n\nstd::vector<machineMap> mapping(numMachines, machineMap(numTokens));\nfor (subMapping : mapping) {\nfor (pair : subMapping) {\nstd::cin >> pair.first >> pair.second;\n}\n}\n\nauto currentPos = std::make_pair(0, firstMachine);\nfor (size_t step = 0; step < numSteps; ++step) {\ncurrentPos = mapping[currentPos.second][currentPos.first];\n}\nstd::cout << currentPos.second+1 << std::endl;\n}\n\n\nSo this would be the plain algorithm you utilized. However, as you said this will most likely give you TLE. So what i believe would be the main idea behind the challenge is to realize that there might be immutable orbits inside the map, aka whenever you end up with the same combination of token and machine, you can shortcircuit by taking the remaining number of steps modulo the number of steps it takes you to reach the node the again.\n\nSo the question is, how can you find out, whether you can shortcuircuit and how long it took to get to the same token again. For me the solution would be not use a std::pair, but rather a custom struct\n\nstruct mapEntry {\nsize_t nextToken = 0;\nsize_t nextMachine = 0;\nbool visited = false;\nsize_t lastVisited = 0;\n}\n\n\nNow the code would look like this:\n\n#include <iostream>\n#include <vector>\n\nstruct mapEntry {\nsize_t nextToken = 0;\nsize_t nextMachine = 0;\nbool visited = false;\nsize_t lastVisited = 0;\n}\n\nint main() {\nusing machineMap = std::vector<mapEntry>;\nsize_t numMachines , numTokens , firstMachine , numSteps;\nstd::cin >> numMachines >> numTokens >> firstMachine >> numSteps;\nfirstMachine--;\n\nstd::vector<machineMap> mapping(numMachines, machineMap(numTokens));\nfor (subMapping : mapping) {\nfor (entry : subMapping) {\nstd::cin >> entry.nextToken >> entry.nextMachine;\n}\n}\n\nmapEntry currentPos = mapping[firstMachine];\ncurrentPos.visited = true;\ncurrentPos.lastVisited = 0;\n\nfor (size_t step = 1; step < numSteps; ++step) {\ncurrentPos = mapping[currentPos.nextMachine][currentPos.nextToken];\n\nif (currentPos.visited) {\nsize_t cycleLength = step - lastVisited;\nsize_t remainingSteps = (numSteps - step)%cycleLength;\n/* Only loop to remainingStep-1 so that you get the final machine via currentPos.nextMachine */\nfor (size_t newStep = 0; newStep < remainingSteps -1; ++newStep) {\ncurrentPos = mapping[currentPos.nextMachine][currentPos.nextToken];\n}\nbreak;\n} else {\ncurrentPos.visited = true;\ncurrentPos.lastVisited = step;\n}\n}\nstd::cout << currentPos.nextMachine << \"\\n\";\n}\n\n• I think it can be done without a custom struct – hellozee Oct 30 '16 at 3:04\n\n### Cycle detection\n\nWith $M$ machines and $T$ tokens, there are $M*T$ states that you can be in. So your path can be at most $M*T$ moves long before it starts to cycle.\n\nTo solve the problem for large values of $N$, you should first manually make $M*T$ moves. Then, remembering your location (meaning the machine AND token), count how many moves it takes until you end up at the same location again. This is the length of the cycle you are in. After that, you need to make some more final moves to end up at the destination. If n is the original number of moves you needed to make, and cycleLen is the cycle length, then you need to make (n - m*t) % cycleLen more final moves.\n\nThis algorithm makes at most $3*M*T$ moves.\n\n### Sample Implementation\n\nHere is an implementation of the above:\n\n#include <iostream>\n#include <vector>\n\nint main(){\nint machines , tokens , start , end;\nint total;\nstd::cin >> machines >> tokens >> start >> end;\ntotal = machines * tokens;\nstart--;end--;\nstd::vector<std::vector<int> >tokenTable(machines,std::vector<int>(tokens));\nstd::vector<std::vector<int> >machTable(machines,std::vector<int>(tokens));\nstd::vector<int>visitedMach;\nfor(int i=0;i<machines;i++){\nfor(int j=0;j<tokens;j++){\nint tok , mach;\nstd::cin >> tok >> mach;\ntok--;mach--;\ntokenTable[i][j] = tok;\nmachTable[i][j] = mach;\n}\n}\n\nint token = 0;\n\n// If there are a lot of moves, then find a cycle first and then reduce\n// the number of moves to something less than the cycle length.\nif (end > total * 3) {\n// First, make M*T moves.\nfor (int moves = 0; moves < total; moves++) {\nint newTok = tokenTable[start][token];\nint newStart = machTable[start][token];\ntoken = newTok;\nstart = newStart;\n}\n// Next, count the number of moves until we reach this spot again.\nint cycleStart = start;\nint cycleToken = token;\nint cycleLength = 0;\ndo {\nint newTok = tokenTable[start][token];\nint newStart = machTable[start][token];\ntoken = newTok;\nstart = newStart;\ncycleLength++;\n} while (start != cycleStart || token != cycleToken);\n// Now, we can reduce the number of total moves.\nend = (end - total) % cycleLength;\n}\n\n// Now make moves until we reach the end.\nfor (int moves = 0; moves < end; moves++) {\nint newTok = tokenTable[start][token];\nint newStart = machTable[start][token];\ntoken = newTok;\nstart = newStart;\n}\nstd::cout << start+1 << std::endl;\nreturn 0;\n}\n\n• looks alright but kinda confusing for implementation , can you shed some light? – hellozee Nov 6 '16 at 13:45" ]

[ null, "https://i.stack.imgur.com/rNRGp.png", null ]

[ "# From Year 7 to Year 13…\n\nSuch a busy week…\n\nBut I have written a weekly blog post since January 2011 when I made a New Year resolution to write a blog post every week, a habit I don’t intend to stop, so this week I simply offer two slideshows I created for my students recently.\n\nWith Year 7 (age 11-12) we have been studying Algebra. When solving equations, I included for a class of high ability students, equations with the unknown on both sides. Having given them one homework where they were exploring various resources for practising solving equations, a sudent asked in a comment on our homework blog how to use Duncan Keith’s excellent linear equation calculator for practising this type of equation:\n\nThe slideshow below shows how to use the calculator to solve equations where the unknown is on both sides.\n\n.\nAt the other end of the school, with Year 13 I had completed the various integration techniques required for our exam specification. Aware that students sometimes muddle differentiation and integration, I started the last lesson of the series with one of my ‘self-checks’ / mini tests to see what they could easily recall. I have stressed the importance of knowing the basics with this group. The questions I used are presented in the following slide show – a sort of KS5 mental Calculus test!" ]

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[ "# Ultimate Oscillator and Chaikin Oscillator plus Money Flow\n\nFor this post we are looking at Larry Williams Ultimate Oscillator and the Marc Chaikin Oscillator.\n\nDeveloped by Larry Williams the Ultimate Oscillator is a momentum oscillator designed to capture momentum across three different timeframes. The multiple timeframe objective seeks to avoid the pitfalls of other oscillators. The Ultimate Oscillator attempts to correct this fault by incorporating longer timeframes into the basic formula. Williams identified a buy signal a based on a bullish divergence and a sell signal based on a bearish divergence.\n\nThe formula looks like this:\n\n```BP:= Close(@) - Minimum(Low(@),Close(@)[-1]); TR:= Maximum(High(@),Close(@)[-1]) - Minimum(Low(@),Close(@)[-1]); AV7:= Sum(BP,7) / Sum(TR,7)  ; AV14:= Sum(BP,14) / Sum(TR,14)  ; AV28:= Sum(BP,28) / Sum(TR,28)  ; UO:= 100 * ((4*AV7)+(2*AV14)+(AV28))/7;```", null, "Developed by Marc Chaikin, the Chaikin Oscillator measures the momentum of the Accumulation Distribution. This makes it an indicator of an indicator. The Chaikin Oscillator is the difference between the 3-day EMA of the Accumulation Distribution Line and the 10-day EMA of the Accumulation Distribution Line.\n\nLike other momentum indicators, this indicator is designed to anticipate directional changes in the Accumulation Distribution Line by measuring the momentum behind the movements. A momentum change is seen as the first step to a trend change. Anticipating trend changes in the Accumulation Distribution Line can help chartists anticipate trend changes in the underlying market.\n\nAs CQG already has the AD Study available, the formula is really simple:\n\n`MA(A_D(@),Exp,EMA1) - MA(A_D(@),Exp,EMA2)`", null, "While we are talking about Chaikin, one of his widely spread indicators is the Chaikin Money Flow index, which I have added to the pac as well.\n\nChaikin Money Flow measures the amount of Money Flow Volume over a specific period. Money Flow Volume forms the basis for the Accumulation Distribution Line. Instead of a cumulative total of Money Flow Volume, Chaikin Money Flow simply sums Money Flow Volume for a specific look-back period, typically 20 or 21 days. The resulting indicator fluctuates above/below the zero line just like an oscillator.\n\nFormula:\n\n```MFM:= ((Close(@)-Low(@))-(High(@)-Close(@)))/(High(@)-Low(@)); MFV:= MFM*Vol(@); CFM:=Sum(MFV,SUMPeriod)/Sum(Vol(@),SUMPeriod); CFM```", null, "" ]

[ null, "https://news.cqg.com/sites/default/files/images/hm_20190307_1.jpg", null, "https://news.cqg.com/sites/default/files/images/hm_20190307_2.jpg", null, "https://news.cqg.com/sites/default/files/images/hm_20190307_3.jpg", null ]

[ "# Difference between revisions of \"2015 AMC 8 Problems/Problem 5\"\n\n## Problem\n\nBilly's basketball team scored the following points over the course of the first", null, "$11$ games of the season. If his team scores", null, "$40$ in the", null, "$12^{th}$ game, which of the following statistics will show an increase?", null, "$$42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73$$", null, "$\\textbf{(A) } \\text{range} \\qquad \\textbf{(B) } \\text{median} \\qquad \\textbf{(C) } \\text{mean} \\qquad \\textbf{(D) } \\text{mode} \\qquad \\textbf{(E) } \\text{mid-range}$\n\n## Solutions\n\n### Solution 1\n\nWhen they score a", null, "$40$ on the next game, the range increases from", null, "$73-42=31$ to", null, "$73-40=33$. This means the", null, "$\\boxed{\\textbf{(A) } \\text{range}}$ increased.\n\n### Solution 2\n\nBecause", null, "$40$ is less than the score of every game they've played so far, the measures of center will never rise. Only measures of spread, such as the", null, "$\\boxed{\\textbf{(A)}~\\text{range}}$, may increase.\n\n## Video Solution\n\n~savannahsolver\n\n 2015 AMC 8 (Problems • Answer Key • Resources) Preceded byProblem 4 Followed byProblem 6 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AJHSME/AMC 8 Problems and Solutions\n\nThe problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.", null, "" ]

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[ "# Essay introduction sample\n\nWriting an introductory paragraph is easier than it may seem. The key to a successful intro is knowing the components that go into it. Much like a watch has  ... Step 6: Write introduction and conclusion | The Learning Centre ... 21 Apr 2015 ... ... State the parameters of the essay,; Discuss assumptions,; Present a problem. The following examples from Model Essays One and Two show ...\n\nIntroductions to Argumentative Essays Task 3: The four parts of an introduction (again) Print out the answer to task 2. Then circle the sentences which cover each of the four parts of argumentative essay introductions and write the number for each part in the margin next to it, just as you did for the introduction to the marine parks essay in Task 1. Check your answer here Introduction Paragraphs - Mesa Community College Question: How is this a graphical representation of an introduction Paragraph? Answer: Because it starts broad, and gradually narrows towards a focused, but not overly specific thesis. The thesis is specific enough to fully explore the essay, but it's not so specific that there is nothing more to write about. Sample Introduction Paragraph..... Essay Examples | Free Sample essays\n\n## Write a Great First Sentence and Introductory Paragraph\n\nHow to Write an Introduction to Essay. The main purpose of the introduction is to give the reader a clear idea of the essay's focal point. It must get the reader's attention as it is the part when he decides if the essay is worth reading till the end or not. Introductory Paragraph Examples for Essays Introductory Paragraph Examples for Essays. If you want to know how to write great introductory paragraphs for your essays, start training yourself using well-written introduction paragraph examples for essays. An introductory paragraph is first paragraph in an essay, follow the link for more information. It is the paragraph that acts like the ... General Essay Writing Tips - Essay Writing Center Check out our Sample Essay section where you can see scholarship essays, admissions essays, and more! The principle purpose of the introduction is to present your position (this is also known as the \"thesis\" or \"argument\") on the issue at hand but effective introductory paragraphs are so much more than that. How to Write a Process Essay: 30 Exciting Topic Ideas and ...\n\n### Sample Reflective Essay - Example #1 - English Program - CSU ...\n\nSample essay - Online Learning Resources Key words: academic essay, essay question, paragraph, introduction, body, conclusion, reference list Sometimes a good example of what you are trying to achieve is worth a 1000 words of advice! When you are asked to write an essay, try to find some samples (models) of similar writing and learn to observe the craft of the writer.\n\n### Tips from your Tutor: How to Write the Perfect Law Essay ...\n\nEssay introduction targets three objectives: provide the context, define the main focus, idea of the study and briefly outline the structure of your paper. essay intro examples – dovoz\n\n## How to Write the Introduction of an Essay | Owlcation\n\nThe first sentence of the essay is the most important one as its intention is to grab the attention of the reader. The essay introduction examples serve as the essay's \"map.\" PDF Writing introductions and conclusions for essays Update 270912\n\nEssay introduction - OWLL - Massey University Does the essay answer several related questions one after the other (sequential)? Do the paragraphs describe two elements and them compare them (contrasting)? The essay will be much more readable once the reader knows what to expect from the body paragraphs. Introduction examples. See sample essay 1 and sample essay 2 for model introductions. Introduction to Computer Essay | Examples and Samples" ]

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[ "# Book:Ralph J. Smith/Circuits, Devices and Systems/Third Edition\n\n## Ralph J. Smith: Circuits, Devices and Systems (3rd Edition)\n\nPublished $\\text {1976}$\n\n### Contents\n\nPreface\nPart $\\text {I}$ Circuits\n$1$. Electrical Quantities\n$2$. Circuit Principles\n$3$. Signal Waveforms\n$4$. Natural Response\n$5$. Forced Response\n$6$. Complete Response\n$7$. Steady-State AC Circuits\n$8$. General Network Analysis\n$9$. Introduction to Systems\n\nPart $\\text {II}$ Electronic Devices\n$10$. Electron Tubes\n$11$. Semiconductor Diodes\n$12$. Diode Applications\n$13$. Transistors and Integrated Circuits\n$14$. Digital Devices\n$15$. Logic Circuits\n$16$. Amplifier Bias and Large-Signal Performance\n$17$. Small-Signal Models\n$18$. Small-Signal Amplifiers\n$19$. Operational Amplifiers\n\nPart $\\text {III}$ Electromechanical Devices\n$20$. Energy Conversion Phenomena\n$21$. Magnetic Fields and Circuits\n$22$. Transformers\n$23$. Principles of Electromechanics\n$24$. Direct-Current Machines\n$25$. Alternating Current Machines\n$26$. Automatic Control Systems\n$27$. Instruments and Instrumentation Systems\nAppendix\nIndex\n\nNext\n\nFrom Next:\n\nFrom start:" ]

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[ "A REV-scale assessment of metal foam porosity effect on a PCM’s melting in an latent heat energy storage unit\n\nRiheb Mabrouk1, ⋆\n: [email protected]\n1 Laboratoire d’Études des Systèmes Thermiques et Énergétiques (LESTE), École Nationale d’Ingénieurs de Monastir, Rue Ibn Jazza, 5019 Monastir\nMots clés : Phase change material, Forced convection, Porous metal foams, Thermal lattice Boltzmann method\nRésumé :\n\nLatent heat thermal energy storage (LHTES) has become both a promising and attractive thermal energy storage (TES) method that can achieve high energy storage density and near constant temperature during operation while balancing the gap between energy supply and demand.\n\nThis paper deals with the numerical investigation of the enhancement of heat transfer under forced convection in an open-ended horizontal channel filled with a porous structure (metal foam) and a phase change material (PCM: paraffin). The Forchheimer-Brinkman extended Darcy unsteady flow model (generalized Navier-Stokes equations) is assumed to simulate flow and heat transfer occurring within the porous medium for an unsteady forced convection. These are completed by two energy equations based on the local thermal non-equilibrium (LTNE) condition.\n\nSimulations are done using the thermal Single Relaxation Time (T-SRT) lattice Boltzmann Method (LBM) at the representative elementary volume (REV) scale. All lattice Boltzmann equations (LBE) involved are discretized according to the D2Q9 model using three distribution functions. Numerical results were performed to present the effects of porosities (0.5-0.9) on the dynamic and thermal fields, Bejan number and melting front for the sequent Re range (200-400) during charging (melting) process.\n\nThe reliability of the implemented in-house code has been evinced through a comparison of some preliminary results with some results from the literature. Based on the results achieved, it can be stated that the melting process under laminar forced convection is speeded up by decreasing the porosity (=0.5) and increasing the Reynolds number. In addition, high porosity (=0.9) decelerates the front progression owing to the permeability of the metal structure. While, increasing the porosity intensifies the thermal conductivity of the medium and then, induces more energy stored in a short time within the same volume of the support. Thereby, at high Re (=400), it can be stated that the melting phenomenon rate is much faster owing the interstitial heat transfer. However, the heat transfer irreversibility dominates the overall irreversibility of the system.\n\nFinally, it can be concluded that the implemented thermal lattice Boltzmann method represents an appropriate tool that can handle unsteady forced convection melting problems in latent energy storage unit." ]

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[ "TWiki>", null, "Main Web>PressureProblem (2011-01-17, RuggeroPoletto)", null, "", null, "## URANS channel simulation\n\n The simulation performed is a URANS one - K-omega turbulence model - where the inlet condition is defined as a constant massflow for the initial 3000 time steps, and then a sinusoidal fluctuation starts. This leads to a fluctuating massflow rate.", null, "The pressure shows a very strange behaviour: when the sinusoidal massflow begins there is a pressure jump! There seems to be a connection between the pressure instantaneous value and the massflow derivative (although theoretical considerations do not confirm it!!!) which gives us some negative inlet pressure for some time steps: behaviour non-physical, while the pressure average value seems to be influenced by the velocity (as Bernoulli states!!) A GIF animated picture lets understand more easily the pressure problem.", null, "I though the cause of the positive pressure gradient may be traced back to a non predictable behaviour of the shear stresses (the pressure in fact has to equilibrate the losses generated by these stresses). The following graphs shows the shear stresses integral!!", null, "", null, "Something has to be sure: the pressure gradient must balance all the losses subjected to the fluid! Among these losses there are, of course, the wall shear stresses, which basically subtracts momentum to the fluid!! But there are internal losses as well: the turbulence model in fact introduces the term which expresses an energy transfer mechanism from the mean flow to the single particles through a series of vortexes (...). In my mind it was not perfectly clear the influence an instantaneous modification of the flow field (since we are varying the inlet and the flow is incompressible we are basically applying a new massflow along the whole channel) to this term: basically I was wondering if such variation might affect the . To find out an easy answer I run a simulation without any turbulence model (laminar simulation) and ...", null, "in here a further simulation result: the inlet is here define to be constant for 3000 iterations and then it is instantaneously increased. The pressure showed as earlier a behaviour influenced by the derivative of the mass flow!\n\n## A possible explanation ?!?!\n\nIn these days I went through the equations solved and in particular the meaning of each of their terms!!\n\nSomething has to be sure: the pressure gradient must balance all the losses subjected to the fluid! Among these losses there are, of course, the wall shear stresses, which basically subtracts momentum to the fluid!! But there are internal losses as well: the turbulence model in fact introduces the", null, "term which expresses an energy transfer mechanism from the mean flow to the single particles through a series of vortexes (...). In my mind it was not perfectly clear the influence an instantaneous modification of the flow field (since we are varying the inlet and the flow is incompressible we are basically applying a new massflow along the whole channel) to this term: basically I was wondering if such variation might affect the", null, ". To find out an easy answer I run a simulation without any turbulence model (laminar simulation) and ...", null, "The first conclusion is that this behaviour is not affected by the turbulence model!!\n\nWhere can it come from then?\n\nAnother idea I had: the code solves basically a Poisson equation for the pressure, which comes from the navier-stokes and the continuity ones! The equation is here written:", null, "The term on the right side of this equation is zero in a steady channel flow (since", null, ", except i=1 and j=2 - the initial part of the channel must not be considered!). When a variable mass flow is introduced, the right term is no more zero (and this lead to a different pressure distribution compared to the steady case) and we have a dependency with the velocity derivatives (highlighted earlier in some graphs).\n\nMy question is now: are all these considerations correct? If so: I am not able to find an explanation to the \"energy gain\" the flow seems to deal with (...)!\n\nCurrent Tags:\ncreate new tag\n, view all tags\nTopic revision: r6 - 2011-01-17 - 16:57:13 - RuggeroPoletto\nMain Web\n18 Mar 2019\n\nManchester CfdTm\nCode_Saturne\n\nATAAC\nKNOO\n\nDESider\nFLOMANIA" ]

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[ "Sei sulla pagina 1di 10\n\n# MULTIVARIATE TIME SERIES MODELS\n\n332\n\nFrom these results we have to choose the number of cointegrating vectors. Given our\nprevious results it is somewhat surprising that Johansens tests seem to indicate the\npresence of two cointegrating relationships. In the rst EngleGranger steps, we could\nnot reject no-cointegration in any of the cases we considered. A possible explanation\nfor this nding may be that the number of lags in the VAR is too small. Similar to\nwhat we found before with the univariate unit root tests on pt and pt , the inclusion of\ntoo few lags may lead to the wrong conclusion that the series are stationary, or in\nthis case are cointegrated.17 Table 9.11 shows what happens if we repeat the above\nprocedure with a lag length of p = 12, motivated by the fact that we have monthly data.\nWhat is quite clear from these results is that the evidence in favour of one or two\ncointegrating vectors is much weaker than before. The rst test that considers the null\nhypothesis of no cointegration (r = 0) versus the alternative of one cointegrating relationship (r = 1) does not lead to rejection of the null. The second test though, implies\na marginal rejection of the hypothesis of the existence of zero or one cointegrating\nvector. Suppose we continue our analysis despite our reservations, while we decide\nthat the number of cointegrating vectors is equal to one (r = 1). The next part of the\nresults consists of the estimated cointegrating vector , presented in Table 9.12. The\nnormalized cointegrating vector is given in the third column and corresponds to\nst = 6.347pt 14.755pt ,\n\n(9.54)\n\n## which does not seem to correspond to an economically interpretable long-run relationship.\n\nAs the conclusion that there exists one cointegrating relationship between our three\nvariables is most probably incorrect, we do not pursue this example any further. To\nappropriately test for long-run purchasing power parity via the Johansen procedure,\nwe will probably need longer time series. Alternatively, some authors use several\nTable 9.11\n\n## Maximum eigenvalue tests for cointegration\n\nNull hypothesis\n\nAlternative\n\nmax -statistic\n\n5% critical value\n\nH0 : r = 0\nH0 : r 1\nH0 : r 2\n\nH1 : r = 1\nH1 : r = 2\nH1 : r = 3\n\n19.521\n16.437\n6.180\n\n22.04\n15.87\n9.16\n\n## lag length p = 12 intercepts included T = 174\n\nEstimated eigenvalues: 0.1061, 0.0901, 0.0349\nTable 9.12\n\nVariable\nst\npt\npt\n\nNormalized\n0.092\n0.583\n1.354\n\n1.000\n6.347\n14.755\n\n## Based on VAR with p = 12\n\n17\n\nNote, for example, that the cointegrating vector (0, 0, 1)\u0005 corresponds to stationarity of the last element.\n\n## ILLUSTRATION: MONEY DEMAND AND INFLATION\n\n333\n\nsets of countries simultaneously and apply panel data cointegration techniques (see\nChapter 10). Another problem may lie in measuring the two price indices in an accurate\nway, comparable across the two countries.\n\n9.6\n\n## One of the advantages of cointegration in multivariate time series models is that it\n\nmay help improving forecasts. The reason is that forecasts from a cointegrated system\nare tied together by virtue of the existence of one or more long-run relationships.\nTypically, this advantage is realized when forecasting over medium or long horizons (compare Engle and Yoo, 1987). Hoffman and Rasche (1996) and Lin and Tsay\n(1996) empirically examine the forecast performance in a cointegrated system. In this\nsection, based on the Hoffman and Rasche study, we consider an empirical example\nconcerning a ve-dimensional vector process. The empirical work is based on quarterly data for the United States from 1954:1 to 1994:4 (T = 164) for the following\nvariables:18\nmt : log of real M1 money balances\nin t : quarterly ination rate (in % per year)\ncpr t : commercial paper rate\nyt : log real GDP (in billions of 1987 dollars)\ntbr t : treasury bill rate\nThe commercial paper rate and the treasury bill rate are considered as risky and riskfree returns on a quarterly horizon, respectively. The series for M1 and GDP are\nseasonally adjusted. Although one may dispute the presence of a unit root in some of\nthese series, we shall follow Hoffman and Rasche (1996) and assume that these ve\nvariables are all well described by an I (1) process.\nA priori one could think of three possible cointegrating relationships governing the\nlong-run behaviour of these variables. First, we can specify an equation for money\ndemand as\nmt = 1 + 14 yt + 15 tbr t + 1t ,\nwhere 14 denotes the income elasticity and 15 the interest rate elasticity. It can be\nexpected that 14 is close to unity, corresponding to a unitary income elasticity, and\nthat 15 < 0. Second, if real interest rates are stationary we can expect that\nin t = 2 + 25 tbr t + 2t\ncorresponds to a cointegrating relationship with 25 = 1. This is referred to as the\nFisher relation, where we are using actual ination as a proxy for expected ination.19\nThird, it can be expected that the risk premium, as measured by the difference between\n18\n19\n\n## The data are available in the les MONEY.\n\nThe real interest rate is dened as the nominal interest rate minus the expected ination rate.\n\n334\n\n## Table 9.13 Univariate cointegrating regressions by OLS (standard errors\n\nin parentheses), intercept estimates not reported\nMoney demand\nmt\nin t\ncpr t\nyt\ntbr t\nR2\ndw\n\n1\n0\n0\n0.423\n(0.016)\n0.031\n(0.002)\n0.815\n0.199\n3.164\n\nFisher equation\n0\n1\n0\n0\n0.558\n(0.053)\n0.409\n0.784\n1.888\n\n0\n0\n1\n0\n1.038\n(0.010)\n0.984\n0.705\n3.975\n\nthe commercial paper rate and the treasury bill rate, is stationary, so that a third\ncointegrating relationship is given by\ncpr t = 3 + 35 tbr t + 3t\nwith 35 = 1.\nBefore proceeding to the vector process of these ve variables, let us consider the\nOLS estimates of the above three regressions. These are presented in Table 9.13. To\nease comparison with later results the layout stresses that the left-hand side variables\nare included in the cointegrating vector (if it exists) with a coefcient of 1. Note\nthat the OLS standard errors are inappropriate if the variables in the regression are\nintegrated. Except for the risk premium equation, the R 2 s are not close to unity, which\nis an informal requirement for a cointegrating regression. The DurbinWatson statistics\nare small and if the critical values from Table 9.3 are appropriate, we would reject the\nnull hypothesis of no cointegration at the 5% level for the last two equations but not for\nthe money demand equation. Recall that the critical values in Table 9.3 are based on\nthe assumption that all series are random walks, which may be correct for interest rate\nseries but may be incorrect for money supply and GDP. Alternatively, we can test for\na unit root in the residuals of these regressions by the augmented DickeyFuller tests.\nThe results are not very sensitive to the number of lags that is included and the test\nstatistics for 6 lags are reported in Table 9.13. The 5% asymptotic critical value from\nTable 9.2 is given by 3.77 for the regression involving three variables and 3.37 for\nthe regressions with two variables. Only for the risk premium equation we can thus\nreject the null hypothesis of no cointegration.\nThe empirical evidence for the existence of the suggested cointegrating relationships\nbetween the ve variables is somewhat mixed. Only for the risk premium equation we\nnd an R 2 close to unity, a sufciently high DurbinWatson statistic and a signicant\nrejection of the ADF test for a unit root in the residuals. For the two other regressions\nthere is little reason to reject the null hypothesis of no cointegration. Potentially this is\ncaused by the lack of power of the tests that we employ, and it is possible that a multivariate vector analysis provides stronger evidence for the existence of cointegrating\nrelationships between these ve variables. Some additional information is provided\nif we plot the residuals from these three regressions. If the regressions correspond\n\n335\n\n0.15\n0.10\n0.05\n0.00\n0.05\n0.10\n0.15\n55\n\n60\n\n65\n\n70\n\n75\n\n80\n\n85\n\n90\n\n8\n6\n4\n2\n0\n2\n4\n55\n\n60\n\n65\n\nFigure 9.2\n\n70\n\n75\n\n80\n\n85\n\n90\n\n## to cointegration these residuals can be interpreted as long-run equilibrium errors and\n\nshould be stationary and uctuating around zero. For the three regressions, the residuals are displayed in Figures 9.1, 9.2 and 9.3, respectively. Although a visual inspection\nof these graphs is ambiguous, the residuals of the money demand and risk premium\nregressions could be argued to be stationary on the basis of these graphs. For the Fisher\nequation, the current sample period provides less evidence of mean reversion.\nThe rst step in the Johansen approach involves testing for the cointegrating rank\nr. To compute these tests we need to choose the maximum lag length p in the vector\nautoregressive model. Choosing p too small will invalidate the tests and choosing\n\n336\n\n1\n55\n\n60\n\n65\n\nFigure 9.3\n\n70\n\n75\n\n80\n\n85\n\n90\n\n## Residuals of risk premium regression\n\np too large may result in a loss of power. In Table 9.14 we present the results20\nof the cointegrating rank tests for p = 5 and p = 6. The results show that there is\nsome sensitivity with respect to the choice of the maximum lag length in the vector\nautoregressions, although qualitatively the conclusion changes only marginally. At the\n5% level all tests reject the null hypotheses of none or one cointegrating relationship.\nThe tests for the null hypothesis that r = 2 only reject at the 5% level, albeit marginally,\nif we choose p = 6 and use the trace test statistic. As before, we need to choose the\ncointegrating rank r from these results. The most obvious choice is r = 2, although\none could consider r = 3 as well (see Hoffman and Rasche, 1996).\nTable 9.14 Trace and maximum eigenvalue tests for cointegration\nTest statistic\nNull hypothesis\n\nAlternative\n\np=5\n\np=6\n\n5% critical value\n\n127.801\n72.302\n35.169\n16.110\n\n75.98\n53.48\n34.87\n20.18\n\n55.499\n37.133\n19.059\n11.860\n\n34.40\n28.27\n22.04\n15.87\n\ntrace -statistic\nH0 :\nH0 :\nH0 :\nH0 :\n\nr\nr\nr\nr\n\n=0\n1\n2\n3\n\nH1 :\nH1 :\nH1 :\nH1 :\n\nr\nr\nr\nr\n\n1\n2\n3\n4\n\nH0 :\nH0 :\nH0 :\nH0 :\n\nr\nr\nr\nr\n\n=0\n1\n2\n3\n\nH1 :\nH1 :\nH1 :\nH1 :\n\nr\nr\nr\nr\n\n=1\n=2\n=3\n=4\n\n108.723\n59.189\n29.201\n13.785\nmax -statistic\n49.534\n29.988\n15.416\n9.637\n\n## intercepts included T = 164\n\n20\n\nThe results reported in this table are obtained from MicroFit 4.0; critical values taken from Table 9.9.\n\n## ILLUSTRATION: MONEY DEMAND AND INFLATION\n\n337\n\nIf we restrict the rank of the long-run matrix to be equal to two we can estimate\nthe cointegrating vectors and the error-correction model by maximum likelihood, following the Johansen procedure. Recall that statistically the cointegrating vectors are\nnot individually dened, only the space spanned by these vectors is. To identify individual cointegrating relationships we thus need to normalize the cointegrating vectors\nsomehow. When r = 2 we need to impose two normalization constraints on each\ncointegrating vector. Note that in the cointegrating regressions in Table 9.13 a number\nof constraints are imposed a priori, including a 1 for the right-hand side variables\nand zero restrictions on some of the other variables coefcients. In the current case\nwe need to impose two restrictions and, assuming that the money demand and risk\npremium relationships are the most likely candidates, we shall impose that mt and\ncpr t have coefcients of 1, 0 and 0, 1, respectively. Economically, we expect that\nin t does not enter in any of the cointegrating vectors. With these two restrictions,\nthe cointegrating vectors are estimated by maximum likelihood, jointly with the coefcients in the vector error-correction model. The results for the cointegrating vectors\nare presented in Table 9.15.\nThe cointegrating vector for the risk premium equation corresponds closely to our\na priori expectations, with the coefcients for in t , yt and tbr t being insignicantly\ndifferent from zero, zero and one, respectively. For the vector corresponding to the\nmoney demand equation in t appears to enter the equation signicantly. Recall that\nmt corresponds to real money demand, which should normally not depend upon the\nination rate. The coefcient estimate of 0.023 implies that, ceteris paribus, nominal money demand (mt + in t ) increases somewhat less than proportionally with the\nination rate.\nIt is possible to test our a priori cointegrating vectors by using likelihood ratio\ntests. These tests require that the model is re-estimated imposing some additional\nrestrictions on the cointegrating vectors. This way we can test the following hypotheses:21\n\nTable 9.15 ML estimates of cointegrating vectors (after normalization) based on VAR with\np = 6 (standard errors in parentheses), intercept\nestimates not reported\n\nmt\nin t\ncpr t\nyt\ntbr t\n\nMoney demand\n\n1\n0.023\n(0.006)\n0\n0.425\n(0.033)\n0.028\n(0.005)\n\n0\n0.041\n(0.031)\n1\n0.037\n(0.173)\n1.017\n(0.026)\n\n## loglikelihood value: 808.2770\n\n21\n\nThe tests here are actually overidentifying restrictions tests (see Chapter 5). We interpret them as regular\nhypotheses tests taking the a priori restrictions in Table 9.15 as given.\n\n## MULTIVARIATE TIME SERIES MODELS\n\n338\n\nH0a : 12 = 0,\nH0b :\n\n14 = 1;\n\n22 = 24 = 0,\n\n25 = 1; and\n\nH0c : 12 = 22 = 24 = 0,\n\n14 = 25 = 1,\n\nwhere 12 denotes the coefcient for in t in the money demand equation and 22 and\n24 are the coefcients for ination and GDP in the risk premium equation, respectively. The loglikelihood values for the complete model, estimated imposing H0a , H0b\nand H0c , respectively, are given by 782.3459, 783.7761 and 782.3196. The likelihood\nratio test statistics, dened as twice the difference in loglikelihood values, for the three\nnull hypotheses are thus given by 51.86, 49.00 and 51.91. The asymptotic distributions\nunder the null hypotheses of the test statistics are the usual Chi-squared distributions, with degrees of freedom given by the number of restrictions that is tested (see\nChapter 6). Compared with the Chi-squared critical values with 3, 2 or 5 degrees of\nfreedom, each of the hypotheses is clearly rejected.\nAs a last step we consider the vector error-correction model for this system. This\ncorresponds to a VAR of order p 1 = 5 for the rst-differenced series, with the\ninclusion of two error-correction terms in each equation, one for each cointegrating\nvector. Note that the number of parameters estimated in this vector error-correction\nmodel is well above 100, so we shall concentrate on a limited part of the results only.\nThe two error-correction terms are given by\necm1t = mt 0.023in t + 0.425yt 0.028tbr t + 3.362;\necm2t = cpr t + 0.041in t 0.037yt + 1.017tbr t + 0.687.\nThe adjustment coefcients in the 5 2 matrix , with their associated standard errors,\nare reported in Table 9.16. The long-run money demand equation contributes signicantly to the short-run movements of both money demand and income. The short-run\nbehaviour of money demand, ination and the commercial paper rate appears to be\nsignicantly affected by the long-run risk premium relationship. There is no statistical\nTable 9.16 Estimated matrix of adjustment\ncoefcients (standard errors in parentheses),\n\n## indicates signicance at the 5% level\n\nError-correction term\nEquation\n\bmt\n\bin t\n\bcpr t\n\byt\n\btbr t\n\necm1t1\n\necm2t1\n\n0.0090\n(0.0024)\n1.1618\n(0.5287)\n0.6626\n(0.2618)\n0.0013\n(0.0028)\n0.3195\n(0.2365)\n\n0.0276\n(0.0104)\n1.4629\n(2.3210)\n2.1364\n(1.1494)\n0.0687\n(0.0121)\n1.2876\n(1.0380)\n\nEXERCISES\n\n339\n\nevidence that the treasury bill rate adjusts to any deviation from long-run equilibria,\nso that it could be treated as weakly exogenous.\n\n9.7\n\nConcluding Remarks\n\nThe literature on cointegration and related issues is of a recent date and still expanding.\nIn this chapter we have been fairly brief on some topics, while other topics have\nbeen left out completely. Fortunately, there exists a substantial number of specialized\ntextbooks on the topic that provide a more extensive coverage. Examples of relatively\nnon-technical textbooks are Mills (1990), Harris (1995), Franses (1998), Patterson\n(2001), and Enders (2004). More technical discussion is available in Lutkepohl (1991),\nCuthbertson, Hall and Taylor (1992), Banerjee et al. (1993), Hamilton (1994), Johansen\n(1995), and Boswijk (1999).\n\nExercises\nExercise 9.1 (Cointegration Theory)\n\na. Assume that the two series yt and xt are I (1) and assume that both yt 1 xt and\nyt 2 xt are I (0). Show that this implies that 1 = 2 , showing that there can be\nonly one unique cointegrating parameter.\nb. Explain intuitively why the Durbin-Watson statistic in a regression of the I (1)\nvariables yt upon xt is informative about the question of cointegration between yt\nand xt .\nc. Explain what is meant by super consistency.\nd. Consider three I (1) variables yt , xt and zt . Assume that yt and xt are cointegrated, and that xt and zt are cointegrated. Does this imply that yt and zt are also\ncointegrated? Why (not)?\nExercise 9.2 (Cointegration)\n\nConsider the following very simple relationship between aggregate savings St and\naggregate income Yt .\nSt = + Yt + t ,\n\nt = 1, . . . , T .\n\n(9.55)\n\nFor some country this relationship is estimated by OLS over the years 19461995\n(T = 50). The results are given in Table 9.17.\nTable 9.17 Aggregate savings explained from aggregate\nincome; OLS results\nVariable\n\nCoefcient\n\nStandard error\n\nt-ratio\n\nconstant\nincome\n\n38.90\n0.098\n\n4.570\n0.009\n\n8.51\n10.77\n\n340\n\n## MULTIVARIATE TIME SERIES MODELS\n\nAssume, for the moment, that the series St and Yt are stationary. (Hint: if needed\nconsult Chapter 4 for the rst set of questions.)\na. How would you interpret the coefcient estimate of 0.098 for the income variable?\nb. Explain why the results indicate that there may be a problem of positive autocorrelation. Can you give arguments why, in economic models, positive autocorrelation\nis more likely than negative autocorrelation?\nc. What are the effects of autocorrelation on the properties of the OLS estimator?\nThink about unbiasedness, consistency and the BLUE property.\nd. Describe two different approaches to handle the autocorrelation problem in the\nabove case. Which one would you prefer?\nFrom now on, assume that St and Yt are nonstationary I (1) series.\ne.\nf.\ng.\nh.\ni.\nj.\nk.\nl.\nm.\nn.\n\nAre there indications that the relationship between the two variables is spurious?\nExplain what we mean by spurious regressions.\nAre there indications that there is a cointegrating relationship between St and Yt ?\nExplain what we mean by a cointegrating relationship.\nDescribe two different tests that can be used to test the null hypothesis that St\nand Yt are not cointegrated.\nHow do you interpret the coefcient estimate of 0.098 under the hypothesis that\nSt and Yt are cointegrated?\nAre there reasons to correct for autocorrelation in the error term when we estimate\na cointegrating regression?\nExplain intuitively why the estimator for a cointegrating parameter is super\nconsistent.\nAssuming that St and Yt are cointegrated, describe what we mean by an errorcorrection mechanism. Give an example. What do we learn from it?\nHow can we consistently estimate an error-correction model?\n\n## Exercise 9.3 (Cointegration Empirical)\n\nIn the les INCOME we nd quarterly data on UK nominal consumption and income,\nfor 1971:1 to 1985:2 (T = 58). Part of these data was used in Exercise 8.3.\n\na.\nb.\nc.\nd.\ne.\n\nf.\n\nTest for a unit root in the consumption series using several augmented\nDickeyFuller tests.\nPerform a regression by OLS explaining consumption from income. Test for\ncointegration using two different tests.\nPerform a regression by OLS explaining income from consumption. Test for\ncointegration.\nCompare the estimation results and R 2 s from the last two regressions.\nDetermine the error-correction term from one of the two regressions and estimate an error-correction model for the change in consumption. Test whether the\nRepeat the last question for the change in income. What do you conclude?\n\n10\n\nModels Based on\nPanel Data\n\nA panel data set contains repeated observations over the same units (individuals,\nhouseholds, rms), collected over a number of periods. Although panel data are typically collected at the micro-economic level, it has become more and more practice to\npool individual time series of a number of countries or industries and analyse them\nsimultaneously. The availability of repeated observations on the same units allows\neconomists to specify and estimate more complicated and more realistic models than\na single cross-section or a single time series would do. The disadvantages are more\nof a practical nature: because we repeatedly observe the same units, it is usually\nno longer appropriate to assume that different observations are independent. This\nmay complicate the analysis, particularly in nonlinear and dynamic models. Furthermore, panel data sets very often suffer from missing observations. Even if these\nobservations are missing in a random way (see below), the standard analysis has to" ]

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[ "### 4.1 Initialization parameters\n\nParameter name Type\n\nDefault\nvalue\n\nExplanation\n\nL .F.\n\nNear-surface adjustment of the mixing length to the Prandtl-layer law.\n\nUsually the mixing length in LES models lLES depends (as in PALM) on the grid size and is possibly restricted further in case of stable stratification and near the lower wall (see parameter wall_adjustment). With adjust_mixing_length = .T. the Prandtl' mixing length lPR = kappa * z/phi is calculated and the mixing length actually used in the model is set l = MIN (lLES, lPR). This usually gives a decrease of the mixing length at the bottom boundary and considers the fact that eddy sizes decrease in the vicinity of the wall.\n\nWarning: So far, there is no good experience with adjust_mixing_length = .T.\n\nWith adjust_mixing_length = .T. and the Prandtl-layer being switched on (see prandtl_layer) '(u*)** 2+neumann' should always be set as the lower boundary condition for the TKE (see bc_e_b), otherwise the near-surface value of the TKE is not in agreement with the Prandtl-layer law (Prandtl-layer law and Prandtl-Kolmogorov-Ansatz should provide the same value for Km). A warning is given, if this is not the case.\n\nalpha_surface\n\nR\n0.0\n\nInclination of the model domain with respect to the horizontal (in degrees).\n\nBy means of alpha_surface the model domain can be inclined in x-direction with respect to the horizontal. In this way flows over inclined surfaces (e.g. drainage flows, gravity flows) can be simulated. In case of alpha_surface /= 0 the buoyancy term appears both in the equation of motion of the u-component and of the w-component.\n\nAn inclination is only possible in case of cyclic horizontal boundary conditions along x AND y (see bc_lr and bc_ns) and topography = 'flat'.\n\nRuns with inclined surface still require additional user-defined code as well as modifications to the default code. Please ask the PALM developer  group.\n\nbc_e_b\n\nC * 20 'neumann'\n\nBottom boundary condition of the TKE.\n\nbc_e_b may be set to 'neumann' or '(u*) ** 2+neumann'. bc_e_b = 'neumann' yields to e(k=0)=e(k=1) (Neumann boundary condition), where e(k=1) is calculated via the prognostic TKE equation. Choice of '(u*)**2+neumann' also yields to e(k=0)=e(k=1), but the TKE at the Prandtl-layer top (k=1) is calculated diagnostically by e(k=1)=(us/0.1)**2. However, this is only allowed if a Prandtl-layer is used (prandtl_layer). If this is not the case, a warning is given and bc_e_b is reset to 'neumann'\n\nAt the top boundary a Neumann boundary condition is generally used: (e(nz+1) = e(nz)).\n\nbc_lr\n\nC * 20 'cyclic' Boundary condition along x (for all quantities).\n\nBy default, a cyclic boundary condition is used along x.\n\nbc_lr may also be assigned the values 'dirichlet/neumann' (inflow from left, outflow to the right) or 'neumann/dirichlet' (inflow from right, outflow to the left). This requires the multi-grid method to be used for solving the Poisson equation for perturbation pressure (see psolver) and it also requires cyclic boundary conditions along y (see\nbc_ns).\n\nIn case of these non-cyclic lateral boundaries, a Dirichlet condition is used at the inflow for all quantities (initial vertical profiles - see initializing_actions - are fixed during the run) except u, to which a Neumann (zero gradient) condition is applied. At the outflow, a Neumann (zero gradient) condition is used for all quantities except v, which is set to its horizontal average along the outflow (e.g. v(k,:,nx+1) = average_along_y( v(k,:,nx)), and except w, which is set to zero (Dirichlet condition). These conditions ensure the velocity field to be free of divergence at the inflow and at the outflow. For perturbation pressure Neumann (zero gradient) conditions are assumed both at the inflow and at the outflow.\n\nWhen using non-cyclic lateral boundaries, a filter is applied to the velocity field in the vicinity of the outflow in order to suppress any reflections of outgoing disturbances (see km_damp_max and outflow_damping_width).\n\nIn order to maintain a turbulent state of the flow, it may be neccessary to continuously impose perturbations on the horizontal velocity field in the vicinity of the inflow throughout the whole run. This can be switched on using create_disturbances. The horizontal range to which these perturbations are applied is controlled by the parameters inflow_disturbance_begin and inflow_disturbance_end. The vertical range and the perturbation amplitude are given by disturbance_level_b, disturbance_level_t, and disturbance_amplitude. The time interval at which perturbations are to be imposed is set by dt_disturb.\n\nIn case of non-cyclic horizontal boundaries call_psolver at_all_substeps = .T. should be used.\n\nNote:\nUsing non-cyclic lateral boundaries requires very sensitive adjustments of the inflow (vertical profiles) and the bottom boundary conditions, e.g. a surface heating should not be applied near the inflow boundary because this may significantly disturb the inflow. Please check the model results very carefully.\n\nbc_ns\n\nC * 20 'cyclic' Boundary condition along y (for all quantities).\n\nBy default, a cyclic boundary condition is used along y.\n\nbc_ns may also be assigned the values 'dirichlet/neumann' (inflow from rear (\"north\"), outflow to the front (\"south\")) or 'neumann/dirichlet' (inflow from front (\"south\"), outflow to the rear (\"north\")). This requires the multi-grid method to be used for solving the Poisson equation for perturbation pressure (see psolver) and it also requires cyclic boundary conditions along x (see\nbc_lr).\n\nIn case of these non-cyclic lateral boundaries, a Dirichlet condition is used at the inflow for all quantities (initial vertical profiles - see initializing_actions - are fixed during the run) except v, to which a Neumann (zero gradient) condition is applied. At the outflow, a Neumann (zero gradient) condition is used for all quantities except u, which is set to its horizontal average along the outflow (e.g. u(k,ny+1,:) = average_along_x( u(k,ny,:)), and except w, which is set to zero (Dirichlet condition). These conditions ensure the velocity field to be free of divergence at the inflow and at the outflow. For perturbation pressure Neumann (zero gradient) conditions are assumed both at the inflow and at the outflow.\n\nFor further details regarding non-cyclic lateral boundary conditions see bc_lr.\n\nbc_p_b\n\nC * 20 'neumann'\n\nBottom boundary condition of the perturbation pressure.\n\nAllowed values are 'dirichlet', 'neumann' and 'neumann+inhomo''dirichlet' sets p(k=0)=0.0,  'neumann' sets p(k=0)=p(k=1). 'neumann+inhomo' corresponds to an extended Neumann boundary condition where heat flux or temperature inhomogeneities near the surface (pt(k=1))  are additionally regarded (see Shen and LeClerc (1995, Q.J.R. Meteorol. Soc., 1209)). This condition is only permitted with the Prandtl-layer switched on (prandtl_layer), otherwise the run is terminated.\n\nSince at the bottom boundary of the model the vertical velocity disappears (w(k=0) = 0.0), the consistent Neumann condition ('neumann' or 'neumann+inhomo') dp/dz = 0 should be used, which leaves the vertical component w unchanged when the pressure solver is applied. Simultaneous use of the Neumann boundary conditions both at the bottom and at the top boundary (bc_p_t) usually yields no consistent solution for the perturbation pressure and should be avoided.\n\nbc_p_t\n\nC * 20 'dirichlet'\n\nTop boundary condition of the perturbation pressure.\n\nAllowed values are 'dirichlet' (p(k=nz+1)= 0.0) or 'neumann' (p(k=nz+1)=p(k=nz)).\n\nSimultaneous use of Neumann boundary conditions both at the top and bottom boundary (bc_p_b) usually yields no consistent solution for the perturbation pressure and should be avoided. Since at the bottom boundary the Neumann condition  is a good choice (see bc_p_b), a Dirichlet condition should be set at the top boundary.\n\nbc_pt_b\n\nC*20 'dirichlet'\n\nBottom boundary condition of the potential temperature.\n\nAllowed values are 'dirichlet' (pt(k=0) = const. = pt_surface + pt_surface_initial_change; the user may change this value during the run using user-defined code) and 'neumann' (pt(k=0)=pt(k=1)).\nWhen a constant surface sensible heat flux is used (surface_heatflux), bc_pt_b = 'neumann' must be used, because otherwise the resolved scale may contribute to the surface flux so that a constant value cannot be guaranteed.\n\nbc_pt_t\n\nC * 20 'neumann'\n\nTop boundary condition of the potential temperature.\n\nAllowed are the values 'dirichlet' (pt(k=nz) and pt(k=nz+1) do not change during the run) and 'neumann'. With the Neumann boundary condition the value of the temperature gradient at the top is calculated from the initial temperature profile (see pt_surface, pt_vertical_gradient) by bc_pt_t_val = (pt_init(k=nz) - pt_init(k=nz-1)) / dzu(nz).\nUsing this value (assumed constant during the run) the temperature boundary values are calculated as\n\npt(k=nz) = pt(k=nz-1) + bc_pt_t_val * dzu(nz)\n\nand\n\npt(k=nz+1) = pt(k=nz) + bc_pt_t_val * dzu(nz+1)\n\n(up to k=nz-1 the prognostic equation for the temperature is solved).\n\nbc_q_b\n\nC * 20 'dirichlet'\n\nBottom boundary condition of the specific humidity / total water content.\n\nAllowed values are 'dirichlet' (q(k=0) = const. = q_surface + q_surface_initial_change; the user may change this value during the run using user-defined code) and 'neumann' (q(k=0)=q(k=1)).\nWhen a constant surface latent heat flux is used (surface_waterflux), bc_q_b = 'neumann' must be used, because otherwise the resolved scale may contribute to the surface flux so that a constant value cannot be guaranteed.\n\nbc_q_t\n\nC * 20 'neumann'\n\nTop boundary condition of the specific humidity / total water content.\n\nAllowed are the values 'dirichlet' (q(k=nz) and q(k=nz+1) do not change during the run) and 'neumann'. With the Neumann boundary condition the value of the humidity gradient at the top is calculated from the initial humidity profile (see q_surface, q_vertical_gradient) by: bc_q_t_val = ( q_init(k=nz) - q_init(k=nz-1)) / dzu(nz).\nUsing this value (assumed constant during the run) the humidity boundary values are calculated as\n\nq(k=nz) = q(k=nz-1) + bc_q_t_val * dzu(nz)\n\nand\n\nq(k=nz+1) =q(k=nz) + bc_q_t_val * dzu(nz+1)\n\n(up tp k=nz-1 the prognostic equation for q is solved).\n\nbc_s_b\n\nC * 20 'dirichlet'\n\nBottom boundary condition of the scalar concentration.\n\nAllowed values are 'dirichlet' (s(k=0) = const. = s_surface + s_surface_initial_change; the user may change this value during the run using user-defined code) and 'neumann' (s(k=0) = s(k=1)).\nWhen a constant surface concentration flux is used (surface_scalarflux), bc_s_b = 'neumann' must be used, because otherwise the resolved scale may contribute to the surface flux so that a constant value cannot be guaranteed.\n\nbc_s_t\n\nC * 20 'neumann'\n\nTop boundary condition of the scalar concentration.\n\nAllowed are the values 'dirichlet' (s(k=nz) and s(k=nz+1) do not change during the run) and 'neumann'. With the Neumann boundary condition the value of the scalar concentration gradient at the top is calculated from the initial scalar concentration profile (see s_surface, s_vertical_gradient) by: bc_s_t_val = (s_init(k=nz) - s_init(k=nz-1)) / dzu(nz).\nUsing this value (assumed constant during the run) the concentration boundary values are calculated as\n\ns(k=nz) = s(k=nz-1) + bc_s_t_val * dzu(nz)\n\nand\n\ns(k=nz+1) = s(k=nz) + bc_s_t_val * dzu(nz+1)\n\n(up to k=nz-1 the prognostic equation for the scalar concentration is solved).\n\nbc_uv_b\n\nC * 20 'dirichlet'\n\nBottom boundary condition of the horizontal velocity components u and v.\n\nAllowed values are 'dirichlet' and 'neumann'. bc_uv_b = 'dirichlet' yields the no-slip condition with u=v=0 at the bottom. Due to the staggered grid u(k=0) and v(k=0) are located at z = - 0,5 * dz (below the bottom), while u(k=1) and v(k=1) are located at z = +0,5 * dz. u=v=0 at the bottom is guaranteed using mirror boundary condition:\n\nu(k=0) = - u(k=1) and v(k=0) = - v(k=1)\n\nThe Neumann boundary condition yields the free-slip condition with u(k=0) = u(k=1) and v(k=0) = v(k=1). With Prandtl - layer switched on, the free-slip condition is not allowed (otherwise the run will be terminated).\n\nbc_uv_t\n\nC * 20 'dirichlet'\n\nTop boundary condition of the horizontal velocity components u and v.\n\nAllowed values are 'dirichlet' and 'neumann'. The Dirichlet condition yields u(k=nz+1) = ug(nz+1) and v(k=nz+1) = vg(nz+1), Neumann condition yields the free-slip condition with u(k=nz+1) = u(k=nz) and v(k=nz+1) = v(k=nz) (up to k=nz the prognostic equations for the velocities are solved).\n\nbuilding_height R 50.0 Height of a single building in m.\n\nbuilding_height must be less than the height of the model domain. This parameter requires the use of topography = 'single_building'.\nbuilding_length_x R 50.0 Width of a single building in m.\n\nCurrently, building_length_x must be at least 3 * dx and no more than nx - 1 ) * dx . This parameter requires the use of topography = 'single_building'.\nbuilding_length_y R 50.0 Depth of a single building in m.\n\nCurrently, building_length_y must be at least 3 * dy and no more than ny - 1 )  * dy. This parameter requires the use of topography = 'single_building'.\nbuilding_wall_left R building centered in x-direction x-coordinate of the left building wall (distance between the left building wall and the left border of the model domain) in m.\n\nCurrently, building_wall_left must be at least 1 * dx and less than ( nx  - 1 ) * dxbuilding_length_x. This parameter requires the use of topography = 'single_building'.\n\nThe default value building_wall_left = ( ( nx + 1 ) * dxbuilding_length_x ) / 2 centers the building in x-direction.\nbuilding_wall_south R building centered in y-direction y-coordinate of the South building wall (distance between the South building wall and the South border of the model domain) in m.\n\nCurrently, building_wall_south must be at least 1 * dy and less than ( ny  - 1 ) * dybuilding_length_y. This parameter requires the use of topography = 'single_building'.\n\nThe default value building_wall_south = ( ( ny + 1 ) * dybuilding_length_y ) / 2 centers the building in y-direction.\ncloud_droplets\nL\n.F.\nParameter to switch on usage of cloud droplets.\n\nCloud droplets require to use the particle package (mrun-option -p particles), so in this case a particle corresponds to a droplet. The droplet features (number of droplets, initial radius, etc.) can be steered with the  respective particle parameters (see e.g. radius). The real number of initial droplets in a grid cell is equal to the initial number of droplets (defined by the particle source parameters pst, psl, psr, pss, psn, psb, pdx, pdy and pdz) times the initial_weighting_factor.\n\nIn case of using cloud droplets, the default condensation scheme in PALM cannot be used, i.e. cloud_physics must be set .F..\n\ncloud_physics\n\nL\n.F.\n\nParameter to switch on the condensation scheme.\n\nFor cloud_physics = .TRUE., equations for the liquid water  content and the liquid water potential temperature are solved instead of those for specific humidity and potential temperature. Note that a grid volume is assumed to be either completely saturated or completely unsaturated (0%-or-100%-scheme). A simple precipitation scheme can additionally be switched on with parameter precipitation. Also cloud-top cooling by longwave radiation can be utilized (see radiation)\n\ncloud_physics =\n.TRUE. requires moisture = .TRUE. .\nDetailed information about the condensation scheme is given in the description of the cloud physics module (pdf-file, only in German).\n\nThis condensation scheme is not allowed if cloud droplets are simulated explicitly (see cloud_droplets).\nconserve_volume_flow L .F. Conservation of volume flow in x- and y-direction.\n\nconserve_volume_flow = .TRUE. guarantees that the volume flow through the xz- or yz-cross-section of the total model domain remains constant (equal to the initial value at t=0) throughout the run.\n\ncut_spline_overshoot\n\nL .T.\n\nCuts off of so-called overshoots, which can occur with the upstream-spline scheme.\n\nThe cubic splines tend to overshoot in case of discontinuous changes of variables between neighbouring grid points. This may lead to errors in calculating the advection tendency. Choice of cut_spline_overshoot = .TRUE. (switched on by default) allows variable values not to exceed an interval defined by the respective adjacent grid points. This interval can be adjusted seperately for every prognostic variable (see initialization parameters overshoot_limit_e, overshoot_limit_pt, overshoot_limit_u, etc.). This might be necessary in case that the default interval has a non-tolerable effect on the model results.\n\nOvershoots may also be removed using the parameters ups_limit_e, ups_limit_pt, etc. as well as by applying a long-filter (see long_filter_factor).\n\ndamp_level_1d\n\nR zu(nz+1)\n\nHeight where the damping layer begins in the 1d-model (in m).\n\nThis parameter is used to switch on a damping layer for the 1d-model, which is generally needed for the damping of inertia oscillations. Damping is done by gradually increasing the value of the eddy diffusivities about 10% per vertical grid level (starting with the value at the height given by damp_level_1d, or possibly from the next grid pint above), i.e. Km(k+1) = 1.1 * Km(k). The values of Km are limited to 10 m**2/s at maximum.\nThis parameter only comes into effect if the 1d-model is switched on for the initialization of the 3d-model using initializing_actions = 'set_1d-model_profiles'.\n\ndissipation_1d\nC*20\n'as_in_3d_\nmodel'\nCalculation method for the energy dissipation term in the TKE equation of the 1d-model.\n\nBy default the dissipation is calculated as in the 3d-model using diss = (0.19 + 0.74 * l / l_grid) * e**1.5 / l.\n\nSetting dissipation_1d = 'detering' forces the dissipation to be calculated as diss = 0.064 * e**1.5 / l.\n\ndt\n\nR variable\n\nTime step for the 3d-model (in s).\n\nBy default, (i.e. if a Runge-Kutta scheme is used, see timestep_scheme) the value of the time step is calculating after each time step (following the time step criteria) and used for the next step.\n\nIf the user assigns dt a value, then the time step is fixed to this value throughout the whole run (whether it fulfills the time step criteria or not). However, changes are allowed for restart runs, because dt can also be used as a run parameter\n\nIn case that the calculated time step meets the condition\n\ndt < 0.00001 * dt_max (with dt_max = 20.0)\n\nthe simulation will be aborted. Such situations usually arise in case of any numerical problem / instability which causes a non-realistic increase of the wind speed.\n\nA small time step due to a large mean horizontal windspeed speed may be enlarged by using a coordinate transformation (see galilei_transformation), in order to spare CPU time.\n\nIf the leapfrog timestep scheme is used (see timestep_scheme) a temporary time step value dt_new is calculated first, with dt_new = cfl_factor * dt_crit where dt_crit is the maximum timestep allowed by the CFL and diffusion condition. Next it is examined whether dt_new exceeds or falls below the value of the previous timestep by at least +5 % / -2%. If it is smaller, dt = dt_new is immediately used for the next timestep. If it is larger, then dt = 1.02 * dt_prev (previous timestep) is used as the new timestep, however the time step is only increased if the last change of the time step is dated back at least 30 iterations. If dt_new is located in the interval mentioned above, then dt does not change at all. By doing so, permanent time step changes as well as large sudden changes (increases) in the time step are avoided.\n\ndt_pr_1d\n\nR 9999999.9\n\nTemporal interval of vertical profile output of the 1D-model (in s).\n\nData are written in ASCII format to file LIST_PROFIL_1D. This parameter is only in effect if the 1d-model has been switched on for the initialization of the 3d-model with initializing_actions = 'set_1d-model_profiles'.\n\ndt_run_control_1d\n\nR 60.0\n\nTemporal interval of runtime control output of the 1d-model (in s).\n\nData are written in ASCII format to file RUN_CONTROL. This parameter is only in effect if the 1d-model is switched on for the initialization of the 3d-model with initializing_actions = 'set_1d-model_profiles'.\n\ndx\n\nR 1.0\n\nHorizontal grid spacing along the x-direction (in m).\n\nAlong x-direction only a constant grid spacing is allowed.\n\ndy\n\nR 1.0\n\nHorizontal grid spacing along the x-direction (in m).\n\nAlong x-direction only a constant grid spacing is allowed.\n\ndz\n\nR\n\nVertical grid spacing (in m).\n\nThis parameter must be assigned by the user, because no default value is given.\n\nBy default, the model uses constant grid spacing along z-direction, but it can be stretched using the parameters dz_stretch_level and dz_stretch_factor. In case of stretching, a maximum allowed grid spacing can be given by dz_max.\n\nAssuming a constant dz, the scalar levels (zu) are calculated directly by:\n\nzu(0) = - dz * 0.5\nzu(1) = dz * 0.5\n\nThe w-levels lie half between them:\n\nzw(k) = ( zu(k) + zu(k+1) ) * 0.5\n\ndz_maxR9999999.9Allowed maximum vertical grid spacing (in m).\n\nIf the vertical grid is stretched (see dz_stretch_factor and dz_stretch_level), dz_max can be used to limit the vertical grid spacing.\n\ndz_stretch_factor\n\nR 1.08\n\nStretch factor for a vertically stretched grid (see dz_stretch_level).\n\nThe stretch factor should not exceed a value of approx. 1.10 - 1.12, otherwise the discretization errors due to the stretched grid not negligible any more. (refer Kalnay de Rivas)\n\ndz_stretch_level\n\nR 100000.0\n\nHeight level above which the grid is to be stretched vertically (in m).\n\nThe vertical grid spacings dz above this level are calculated as\n\nand used as spacings for the scalar levels (zu). The w-levels are then defined as:\n\nzw(k) = ( zu(k) + zu(k+1) ) * 0.5\n\ne_min R 0.0 Minimum subgrid-scale TKE in m2s-2.\n\nThis option adds artificial viscosity to the flow by ensuring that the subgrid-scale TKE does not fall below the minimum threshold e_min.\n\nend_time_1d\n\nR 864000.0\n\nTime to be simulated for the 1d-model (in s).\n\nThe default value corresponds to a simulated time of 10 days. Usually, after such a period the inertia oscillations have completely decayed and the solution of the 1d-model can be regarded as stationary (see damp_level_1d). This parameter is only in effect if the 1d-model is switched on for the initialization of the 3d-model with initializing_actions = 'set_1d-model_profiles'.\n\nfft_method\n\nC * 20 'system-\nspecific'\n\nFFT-method to be used.\n\nThe fast fourier transformation (FFT) is used for solving the perturbation pressure equation with a direct method (see psolver) and for calculating power spectra (see optional software packages, section 4.2).\n\nBy default, system-specific, optimized routines from external vendor libraries are used. However, these are available only on certain computers and there are more or less severe restrictions concerning the number of gridpoints to be used with them.\n\nThere are two other PALM internal methods available on every machine (their respective source code is part of the PALM source code):\n\n1.: The Temperton-method from Clive Temperton (ECWMF) which is computationally very fast and switched on with fft_method = 'temperton-algorithm'. The number of horizontal gridpoints (nx+1, ny+1) to be used with this method must be composed of prime factors 2, 3 and 5.\n\n2.: The Singleton-method which is very slow but has no restrictions concerning the number of gridpoints to be used with, switched on with fft_method = 'singleton-algorithm'.\n\ngalilei_transformation\n\nL .F. Application of a Galilei-transformation to the coordinate system of the model.\n\nWith galilei_transformation = .T., a so-called Galilei-transformation is switched on which ensures that the coordinate system of the model is moved along with the geostrophical wind. Alternatively, the model domain can be moved along with the averaged horizontal wind (see use_ug_for_galilei_tr, this can and will naturally change in time). With this method, numerical inaccuracies of the Piascek - Williams - scheme (concerns in particular the momentum advection) are minimized. Beyond that, in the majority of cases the lower relative velocities in the moved system permit a larger time step (dt). Switching the transformation on is only worthwhile if the geostrophical wind (ug, vg) and the averaged horizontal wind clearly deviate from the value 0. In each case, the distance the coordinate system has been moved is written to the file RUN_CONTROL\n\nNon-cyclic lateral boundary conditions (see bc_lr and bc_ns), the specification of a gestrophic wind that is not constant with height as well as e.g. stationary inhomogeneities at the bottom boundary do not allow the use of this transformation.\n\ngrid_matching\n\nC * 6 'match' Variable to adjust the subdomain sizes in parallel runs.\n\nFor grid_matching = 'strict', the subdomains are forced to have an identical size on all processors. In this case the processor numbers in the respective directions of the virtual processor net must fulfill certain divisor conditions concerning the grid point numbers in the three directions (see nx, ny and nz). Advantage of this method is that all PEs bear the same computational load.\n\nThere is no such restriction by default, because then smaller subdomains are allowed on those processors which form the right and/or north boundary of the virtual processor grid. On all other processors the subdomains are of same size. Whether smaller subdomains are actually used, depends on the number of processors and the grid point numbers used. Information about the respective settings are given in file RUN_CONTROL.\n\nWhen using a multi-grid method for solving the Poisson equation (see psolver) only grid_matching = 'strict' is allowed.\n\nNote:\nIn some cases for small processor numbers there may be a very bad load balancing among the processors which may reduce the performance of the code.\ninflow_disturbance_\nbegin\nI MIN(10,\nnx/2 or ny/2)\nLower limit of the horizontal range for which random perturbations are to be imposed on the horizontal velocity field (gridpoints).\n\nIf non-cyclic lateral boundary conditions are used (see bc_lr or bc_ns), this parameter gives the gridpoint number (counted horizontally from the inflow)  from which on perturbations are imposed on the horizontal velocity field. Perturbations must be switched on with parameter create_disturbances.\ninflow_disturbance_\nend\nI MIN(100,\n3/4*nx or\n3/4*ny)\nUpper limit of the horizontal range for which random perturbations are to be imposed on the horizontal velocity field (gridpoints).\n\nIf non-cyclic lateral boundary conditions are used (see bc_lr or bc_ns), this parameter gives the gridpoint number (counted horizontally from the inflow)  unto which perturbations are imposed on the horizontal velocity field. Perturbations must be switched on with parameter create_disturbances.\n\ninitializing_actions\n\nC * 100\n\nInitialization actions to be carried out.\n\nThis parameter does not have a default value and therefore must be assigned with each model run. For restart runs initializing_actions = 'read_restart_data' must be set. For the initial run of a job chain the following values are allowed:\n\n'set_constant_profiles'\n\n'set_1d-model_profiles'\n\nThe arrays of the 3d-model are initialized with the (stationary) solution of the 1d-model. These are the variables e, kh, km, u, v and with Prandtl layer switched on rif, us, usws, vsws. The temperature (humidity) profile consisting of linear sections is set as for 'set_constant_profiles' and assumed as constant in time within the 1d-model. For steering of the 1d-model a set of parameters with suffix \"_1d\" (e.g. end_time_1d, damp_level_1d) is available.\n\n'initialize_vortex'\n\nThe initial velocity field of the 3d-model corresponds to a Rankine-vortex with vertical axis. This setting may be used to test advection schemes. Free-slip boundary conditions for u and v (see bc_uv_b, bc_uv_t) are necessary. In order not to distort the vortex, an initial horizontal wind profile constant with height is necessary (to be set by initializing_actions = 'set_constant_profiles') and some other conditions have to be met (neutral stratification, diffusion must be switched off, see km_constant). The center of the vortex is located at jc = (nx+1)/2. It extends from k = 0 to k = nz+1. Its radius is 8 * dx and the exponentially decaying part ranges to 32 * dx (see init_rankine.f90).\n\n'initialize_ptanom'\n\nA 2d-Gauss-like shape disturbance (x,y) is added to the initial temperature field with radius 10.0 * dx and center at jc = (nx+1)/2. This may be used for tests of scalar advection schemes (see scalar_advec). Such tests require a horizontal wind profile constant with hight and diffusion switched off (see 'initialize_vortex'). Additionally, the buoyancy term must be switched of in the equation of motion  for w (this requires the user to comment out the call of buoyancy in the source code of prognostic_equations.f90).\n\nValues may be combined, e.g. initializing_actions = 'set_constant_profiles initialize_vortex', but the values of 'set_constant_profiles' and 'set_1d-model_profiles' must not be given at the same time.\n\nkm_constant\n\nR variable\n(computed from TKE)\n\nConstant eddy diffusivities are used (laminar simulations).\n\nIf this parameter is specified, both in the 1d and in the 3d-model constant values for the eddy diffusivities are used in space and time with Km = km_constant and Kh = Km / prandtl_number. The prognostic equation for the subgrid-scale TKE is switched off. Constant eddy diffusivities are only allowed with the Prandtl layer (prandtl_layer) switched off.\n\nkm_damp_max\n\nR 0.5*(dx or dy) Maximum diffusivity used for filtering the velocity field in the vicinity of the outflow (in m2/s).\n\nWhen using non-cyclic lateral boundaries (see bc_lr or bc_ns), a smoothing has to be applied to the velocity field in the vicinity of the outflow in order to suppress any reflections of outgoing disturbances. Smoothing is done by increasing the eddy diffusivity along the horizontal direction which is perpendicular to the outflow boundary. Only velocity components parallel to the outflow boundary are filtered (e.g. v and w, if the outflow is along x). Damping is applied from the bottom to the top of the domain.\n\nThe horizontal range of the smoothing is controlled by outflow_damping_width which defines the number of gridpoints (counted from the outflow boundary) from where on the smoothing is applied. Starting from that point, the eddy diffusivity is linearly increased (from zero to its maximum value given by km_damp_max) until half of the damping range width, from where it remains constant up to the outflow boundary. If at a certain grid point the eddy diffusivity calculated from the flow field is larger than as described above, it is used instead.\n\nThe default value of km_damp_max has been empirically proven to be sufficient.\n\nlong_filter_factor\n\nR 0.0\n\nFilter factor for the so-called Long-filter.\n\nThis filter very efficiently eliminates 2-delta-waves sometimes cauesed by the upstream-spline scheme (see Mahrer and Pielke, 1978: Mon. Wea. Rev., 106, 818-830). It works in all three directions in space. A value of long_filter_factor = 0.01 sufficiently removes the small-scale waves without affecting the longer waves.\n\nBy default, the filter is switched off (= 0.0). It is exclusively applied to the tendencies calculated by the upstream-spline scheme (see momentum_advec and scalar_advec), not to the prognostic variables themselves. At the bottom and top boundary of the model domain the filter effect for vertical 2-delta-waves is reduced. There, the amplitude of these waves is only reduced by approx. 50%, otherwise by nearly 100%.\nFilter factors with values > 0.01 also reduce the amplitudes of waves with wavelengths longer than 2-delta (see the paper by Mahrer and Pielke, quoted above).\n\nmixing_length_1d\nC*20\n'as_in_3d_\nmodel'\nMixing length used in the 1d-model.\n\nBy default the mixing length is calculated as in the 3d-model (i.e. it depends on the grid spacing).\n\nBy setting mixing_length_1d = 'blackadar', the so-called Blackadar mixing length is used (l = kappa * z / ( 1 + kappa * z / lambda ) with the limiting value lambda = 2.7E-4 * u_g / f).\n\nmoisture\n\nL .F.\n\nParameter to switch on the prognostic equation for specific humidity q.\n\nThe initial vertical profile of q can be set via parameters q_surface, q_vertical_gradient and q_vertical_gradient_level.  Boundary conditions can be set via q_surface_initial_change and surface_waterflux.\n\nIf the condensation scheme is switched on (cloud_physics = .TRUE.), q becomes the total liquid water content (sum of specific humidity and liquid water content).\n\nC * 10 'pw-scheme'\n\nAdvection scheme to be used for the momentum equations.\n\nThe user can choose between the following schemes:\n\n'pw-scheme'\n\nThe scheme of Piascek and Williams (1970, J. Comp. Phys., 6, 392-405) with central differences in the form C3 is used.\nIf intermediate Euler-timesteps are carried out in case of timestep_scheme = 'leapfrog+euler' the advection scheme is - for the Euler-timestep - automatically switched to an upstream-scheme.\n\n'ups-scheme'\n\nThe upstream-spline scheme is used (see Mahrer and Pielke, 1978: Mon. Wea. Rev., 106, 818-830). In opposite to the Piascek-Williams scheme, this is characterized by much better numerical features (less numerical diffusion, better preservation of flow structures, e.g. vortices), but computationally it is much more expensive. In addition, the use of the Euler-timestep scheme is mandatory (timestep_scheme = 'euler'), i.e. the timestep accuracy is only of first order. For this reason the advection of scalar variables (see scalar_advec) should then also be carried out with the upstream-spline scheme, because otherwise the scalar variables would be subject to large numerical diffusion due to the upstream scheme.\n\nSince the cubic splines used tend to overshoot under certain circumstances, this effect must be adjusted by suitable filtering and smoothing (see cut_spline_overshoot, long_filter_factor, ups_limit_pt, ups_limit_u, ups_limit_v, ups_limit_w). This is always neccessary for runs with stable stratification, even if this stratification appears only in parts of the model domain.\n\nWith stable stratification the upstream-spline scheme also produces gravity waves with large amplitude, which must be suitably damped (see rayleigh_damping_factor).\n\nImportant: The  upstream-spline scheme is not implemented for humidity and passive scalars (see moisture and passive_scalar) and requires the use of a 2d-domain-decomposition. The last conditions severely restricts code optimization on several machines leading to very long execution times! The scheme is also not allowed for non-cyclic lateral boundary conditions (see bc_lr and bc_ns).\nnetcdf_precision\nC*20\n(10)\nsingle preci-\nsion for all\noutput quan-\ntities\nDefines the accuracy of the NetCDF output.\n\nBy default, all NetCDF output data (see data_output_format) have single precision  (4 byte) accuracy. Double precision (8 byte) can be choosen alternatively.\nAccuracy for the different output data (cross sections, 3d-volume data, spectra, etc.) can be set independently.\n'<out>_NF90_REAL4' (single precision) or '<out>_NF90_REAL8' (double precision) are the two principally allowed values for netcdf_precision, where the string '<out>' can be chosen out of the following list:\n\n 'xy' horizontal cross section 'xz' vertical (xz) cross section 'yz' vertical (yz) cross section '2d' all cross sections '3d' volume data 'pr' vertical profiles 'ts' time series, particle time series 'sp' spectra 'prt' particles 'all' all output quantities\n\nExample:\nIf all cross section data and the particle data shall be output in double precision and all other quantities in single precision, then netcdf_precision = '2d_NF90_REAL8', 'prt_NF90_REAL8' has to be assigned.\n\nnpex\n\nI\n\nNumber of processors along x-direction of the virtual processor net.\n\nFor parallel runs, the total number of processors to be used is given by the mrun option -X. By default, depending on the type of the parallel computer, PALM generates a 1d processor net (domain decomposition along x, npey = 1) or a 2d-net (this is favored on machines with fast communication network). In case of a 2d-net, it is tried to make it more or less square-shaped. If, for example, 16 processors are assigned (-X 16), a 4 * 4 processor net is generated (npex = 4, npey = 4). This choice is optimal for square total domains (nx = ny), since then the number of ghost points at the lateral boundarys of the subdomains is minimal. If nx nd ny differ extremely, the processor net should be manually adjusted using adequate values for npex and npey\n\nImportant: The value of npex * npey must exactly correspond to the value assigned by the mrun-option -X. Otherwise the model run will abort with a corresponding error message.\nAdditionally, the specification of npex and npey may of course override the default setting for the domain decomposition (1d or 2d) which may have a significant (negative) effect on the code performance.\n\nnpey\n\nI\n\nNumber of processors along y-direction of the virtual processor net.\n\nFor further information see npex.\n\nnsor_ini\n\nI 100\n\nInitial number of iterations with the SOR algorithm.\n\nThis parameter is only effective if the SOR algorithm was selected as the pressure solver scheme (psolver = 'sor') and specifies the number of initial iterations of the SOR scheme (at t = 0). The number of subsequent iterations at the following timesteps is determined with the parameter nsor. Usually nsor < nsor_ini, since in each case subsequent calls to psolver use the solution of the previous call as initial value. Suitable test runs should determine whether sufficient convergence of the solution is obtained with the default value and if necessary the value of nsor_ini should be changed.\n\nnx\n\nI\n\nNumber of grid points in x-direction.\n\nA value for this parameter must be assigned. Since the lower array bound in PALM starts with i = 0, the actual number of grid points is equal to nx+1. In case of cyclic boundary conditions along x, the domain size is (nx+1)* dx.\n\nFor parallel runs, in case of grid_matching = 'strict', nx+1 must be an integral multiple of the processor numbers (see npex and npey) along x- as well as along y-direction (due to data transposition restrictions).\n\nny\n\nI\n\nNumber of grid points in y-direction.\n\nA value for this parameter must be assigned. Since the lower array bound in PALM starts with i = 0, the actual number of grid points is equal to ny+1. In case of cyclic boundary conditions along y, the domain size is (ny+1) * dy.\n\nFor parallel runs, in case of grid_matching = 'strict', ny+1 must be an integral multiple of the processor numbers (see npex and npey)  along y- as well as along x-direction (due to data transposition restrictions).\n\nnz\n\nI\n\nNumber of grid points in z-direction.\n\nA value for this parameter must be assigned. Since the lower array bound in PALM starts with k = 0 and since one additional grid point is added at the top boundary (k = nz+1), the actual number of grid points is nz+2. However, the prognostic equations are only solved up to nz (u, v) or up to nz-1 (w, scalar quantities). The top boundary for u and v is at k = nz+1 (u, v) while at k = nz for all other quantities.\n\nFor parallel runs,  in case of grid_matching = 'strict', nz must be an integral multiple of the number of processors in x-direction (due to data transposition restrictions).\n\nomega\n\nR 7.29212E-5\n\nAngular velocity of the rotating system (in rad s-1).\n\nThe angular velocity of the earth is set by default. The values of the Coriolis parameters are calculated as:\n\nf = 2.0 * omega * sin(phi\nf* = 2.0 * omega * cos(phi)\n\noutflow_damping_width\n\nI MIN(20, nx/2 or ny/2) Width of the damping range in the vicinity of the outflow (gridpoints).\n\nWhen using non-cyclic lateral boundaries (see bc_lr or bc_ns), a smoothing has to be applied to the velocity field in the vicinity of the outflow in order to suppress any reflections of outgoing disturbances. This parameter controlls the horizontal range to which the smoothing is applied. The range is given in gridpoints counted from the respective outflow boundary. For further details about the smoothing see parameter km_damp_max, which defines the magnitude of the damping.\n\novershoot_limit_e\n\nR 0.0\n\nAllowed limit for the overshooting of subgrid-scale TKE in case that the upstream-spline scheme is switched on (in m2/s2).\n\nBy deafult, if cut-off of overshoots is switched on for the upstream-spline scheme (see cut_spline_overshoot), no overshoots are permitted at all. If overshoot_limit_e is given a non-zero value, overshoots with the respective amplitude (both upward and downward) are allowed.\n\nOnly positive values are allowed for overshoot_limit_e.\n\novershoot_limit_pt\n\nR 0.0\n\nAllowed limit for the overshooting of potential temperature in case that the upstream-spline scheme is switched on (in K).\n\nFor further information see overshoot_limit_e\n\nOnly positive values are allowed for overshoot_limit_pt.\n\novershoot_limit_u\n\nR 0.0 Allowed limit for the overshooting of the u-component of velocity in case that the upstream-spline scheme is switched on (in m/s).\n\nFor further information see overshoot_limit_e\n\nOnly positive values are allowed for overshoot_limit_u.\n\novershoot_limit_v\n\nR 0.0\n\nAllowed limit for the overshooting of the v-component of velocity in case that the upstream-spline scheme is switched on (in m/s).\n\nFor further information see overshoot_limit_e\n\nOnly positive values are allowed for overshoot_limit_v.\n\novershoot_limit_w\n\nR 0.0\n\nAllowed limit for the overshooting of the w-component of velocity in case that the upstream-spline scheme is switched on (in m/s).\n\nFor further information see overshoot_limit_e\n\nOnly positive values are permitted for overshoot_limit_w.\n\npassive_scalar\n\nL .F.\n\nParameter to switch on the prognostic equation for a passive scalar.\n\nThe initial vertical profile of s can be set via parameters s_surface, s_vertical_gradient and  s_vertical_gradient_level. Boundary conditions can be set via s_surface_initial_change and surface_scalarflux\n\nNote:\nWith passive_scalar switched on, the simultaneous use of humidity (see moisture) is impossible.\n\nphi\n\nR 55.0\n\nGeographical latitude (in degrees).\n\nThe value of this parameter determines the value of the Coriolis parameters f and f*, provided that the angular velocity (see omega) is non-zero.\n\nprandtl_layer\n\nL .T.\n\nParameter to switch on a Prandtl layer.\n\nBy default, a Prandtl layer is switched on at the bottom boundary between z = 0 and z = 0.5 * dz (the first computational grid point above ground for u, v and the scalar quantities). In this case, at the bottom boundary, free-slip conditions for u and v (see bc_uv_b) are not allowed. Likewise, laminar simulations with constant eddy diffusivities (km_constant) are forbidden.\n\nWith Prandtl-layer switched off, the TKE boundary condition bc_e_b = '(u*)**2+neumann' must not be used and is automatically changed to 'neumann' if necessary.  Also, the pressure boundary condition bc_p_b = 'neumann+inhomo'  is not allowed.\n\nThe roughness length is declared via the parameter roughness_length.\n\nprecipitation\n\nL .F.\n\nParameter to switch on the precipitation scheme.\n\nFor precipitation processes PALM uses a simplified Kessler scheme. This scheme only considers the so-called autoconversion, that means the generation of rain water by coagulation of cloud drops among themselves. Precipitation begins and is immediately removed from the flow as soon as the liquid water content exceeds the critical value of 0.5 g/kg.\n\npt_surface\n\nR 300.0\n\nSurface potential temperature (in K).\n\nThis parameter assigns the value of the potential temperature pt at the surface (k=0). Starting from this value, the initial vertical temperature profile is constructed with pt_vertical_gradient and pt_vertical_gradient_level . This profile is also used for the 1d-model as a stationary profile.\n\npt_surface_initial\n_change\n\nR 0.0\n\nChange in surface temperature to be made at the beginning of the 3d run (in K).\n\nIf pt_surface_initial_change is set to a non-zero value, the near surface sensible heat flux is not allowed to be given simultaneously (see surface_heatflux).\n\nR (10) 10 * 0.0\n\nTemperature gradient(s) of the initial temperature profile (in K / 100 m).\n\nThis temperature gradient holds starting from the height  level defined by pt_vertical_gradient_level (precisely: for all uv levels k where zu(k) > pt_vertical_gradient_level, pt_init(k) is set: pt_init(k) = pt_init(k-1) + dzu(k) * pt_vertical_gradient) up to the top boundary or up to the next height level defined by pt_vertical_gradient_level. A total of 10 different gradients for 11 height intervals (10 intervals if pt_vertical_gradient_level(1) = 0.0) can be assigned. The surface temperature is assigned via pt_surface\n\nExample:\n\nThat defines the temperature profile to be neutrally stratified up to z = 500.0 m with a temperature given by pt_surface. For 500.0 m < z <= 1000.0 m the temperature gradient is 1.0 K / 100 m and for z > 1000.0 m up to the top boundary it is 0.5 K / 100 m (it is assumed that the assigned height levels correspond with uv levels).\n\n_level\n\nR (10)\n\n10 *  0.0\n\nHeight level from which on the temperature gradient defined by pt_vertical_gradient is effective (in m).\n\nThe height levels are to be assigned in ascending order. The default values result in a neutral stratification regardless of the values of pt_vertical_gradient (unless the top boundary of the model is higher than 100000.0 m). For the piecewise construction of temperature profiles see pt_vertical_gradient.\n\nq_surface\n\nR 0.0\n\nSurface specific humidity / total water content (kg/kg).\n\nThis parameter assigns the value of the specific humidity q at the surface (k=0).  Starting from this value, the initial humidity profile is constructed with  q_vertical_gradient and q_vertical_gradient_level. This profile is also used for the 1d-model as a stationary profile.\n\nq_surface_initial\n_change\n\nR\n0.0\n\nChange in surface specific humidity / total water content to be made at the beginning of the 3d run (kg/kg).\n\nIf q_surface_initial_change is set to a non-zero value the near surface latent heat flux (water flux) is not allowed to be given simultaneously (see surface_waterflux).\n\nR (10) 10 * 0.0\n\nHumidity gradient(s) of the initial humidity profile (in 1/100 m).\n\nThis humidity gradient holds starting from the height level  defined by q_vertical_gradient_level (precisely: for all uv levels k, where zu(k) > q_vertical_gradient_level, q_init(k) is set: q_init(k) = q_init(k-1) + dzu(k) * q_vertical_gradient) up to the top boundary or up to the next height level defined by q_vertical_gradient_level. A total of 10 different gradients for 11 height intervals (10 intervals if q_vertical_gradient_level(1) = 0.0) can be asigned. The surface humidity is assigned via q_surface.\n\nExample:\n\nThat defines the humidity to be constant with height up to z = 500.0 m with a value given by q_surface. For 500.0 m < z <= 1000.0 m the humidity gradient is 0.001 / 100 m and for z > 1000.0 m up to the top boundary it is 0.0005 / 100 m (it is assumed that the assigned height levels correspond with uv levels).\n\n_level\n\nR (10)\n\n10 *  0.0\n\nHeight level from which on the moisture gradient defined by q_vertical_gradient is effective (in m).\n\nThe height levels are to be assigned in ascending order. The default values result in a humidity constant with height regardless of the values of q_vertical_gradient (unless the top boundary of the model is higher than 100000.0 m). For the piecewise construction of humidity profiles see q_vertical_gradient.\n\nL .F.\n\nParameter to switch on longwave radiation cooling at cloud-tops.\n\nLong-wave radiation processes are parameterized by the effective emissivity, which considers only the absorption and emission of long-wave radiation at cloud droplets. The radiation scheme can be used only with cloud_physics = .TRUE. .\n\nrandom_generator\n\nC * 20\n\n'numerical\nrecipes'\n\nRandom number generator to be used for creating uniformly distributed random numbers.\n\nIt is used if random perturbations are to be imposed on the velocity field or on the surface heat flux field (see create_disturbances and random_heatflux). By default, the \"Numerical Recipes\" random number generator is used. This one provides exactly the same order of random numbers on all different machines and should be used in particular for comparison runs.\n\nBesides, a system-specific generator is available ( random_generator = 'system-specific') which should particularly be used for runs on vector parallel computers (NEC), because the default generator cannot be vectorized and therefore significantly drops down the code performance on these machines.\n\nNote:\nResults from two otherwise identical model runs will not be comparable one-to-one if they used different random number generators.\n\nrandom_heatflux\n\nL .F.\n\nParameter to impose random perturbations on the internal two-dimensional near surface heat flux field shf.\n\nIf a near surface heat flux is used as bottom boundary condition (see surface_heatflux), it is by default assumed to be horizontally homogeneous. Random perturbations can be imposed on the internal two-dimensional heat flux field shf by assigning random_heatflux = .T.. The disturbed heat flux field is calculated by multiplying the values at each mesh point with a normally distributed random number with a mean value and standard deviation of 1. This is repeated after every timestep.\n\nIn case of a non-flat topography, assigning random_heatflux = .T. imposes random perturbations on the combined heat flux field shf composed of surface_heatflux at the bottom surface and wall_heatflux(0) at the topography top face.\n\nrif_max\n\nR 1.0\n\nUpper limit of the flux-Richardson number.\n\nWith the Prandtl layer switched on (see prandtl_layer), flux-Richardson numbers (rif) are calculated for z=zp (k=1) in the 3d-model (in the 1d model for all heights). Their values in particular determine the values of the friction velocity (1d- and 3d-model) and the values of the eddy diffusivity (1d-model). With small wind velocities at the Prandtl layer top or small vertical wind shears in the 1d-model, rif can take up unrealistic large values. They are limited by an upper (rif_max) and lower limit (see rif_min) for the flux-Richardson number. The condition rif_max > rif_min must be met.\n\nrif_min\n\nR - 5.0\n\nLower limit of the flux-Richardson number.\n\nFor further explanations see rif_max. The condition rif_max > rif_min must be met.\n\nroughness_length\n\nR 0.1\n\nRoughness length (in m).\n\nThis parameter is effective only in case that a Prandtl layer is switched on (see prandtl_layer).\n\nC * 10 'pw-scheme'\n\nAdvection scheme to be used for the scalar quantities.\n\nThe user can choose between the following schemes:\n\n'pw-scheme'\n\nThe scheme of Piascek and Williams (1970, J. Comp. Phys., 6, 392-405) with central differences in the form C3 is used.\nIf intermediate Euler-timesteps are carried out in case of timestep_scheme = 'leapfrog+euler' the advection scheme is - for the Euler-timestep - automatically switched to an upstream-scheme.\n\n'bc-scheme'\n\nThe Bott scheme modified by Chlond (1994, Mon. Wea. Rev., 122, 111-125). This is a conservative monotonous scheme with very small numerical diffusion and therefore very good conservation of scalar flow features. The scheme however, is computationally very expensive both because it is expensive itself and because it does (so far) not allow specific code optimizations (e.g. cache optimization). Choice of this scheme forces the Euler timestep scheme to be used for the scalar quantities. For output of horizontally averaged profiles of the resolved / total heat flux, data_output_pr = 'w*pt*BC' / 'wptBC' should be used, instead of the standard profiles ('w*pt*' and 'wpt') because these are too inaccurate with this scheme. However, for subdomain analysis (see statistic_regions) exactly the reverse holds: here 'w*pt*BC' and 'wptBC' show very large errors and should not be used.\n\nThis scheme is not allowed for non-cyclic lateral boundary conditions (see bc_lr and bc_ns).\n\n'ups-scheme'\n\nThe upstream-spline-scheme is used (see Mahrer and Pielke, 1978: Mon. Wea. Rev., 106, 818-830). In opposite to the Piascek Williams scheme, this is characterized by much better numerical features (less numerical diffusion, better preservation of flux structures, e.g. vortices), but computationally it is much more expensive. In addition, the use of the Euler-timestep scheme is mandatory (timestep_scheme = 'euler'), i.e. the timestep accuracy is only first order. For this reason the advection of momentum (see momentum_advec) should then also be carried out with the upstream-spline scheme, because otherwise the momentum would be subject to large numerical diffusion due to the upstream scheme.\n\nSince the cubic splines used tend to overshoot under certain circumstances, this effect must be adjusted by suitable filtering and smoothing (see cut_spline_overshoot, long_filter_factor, ups_limit_pt, ups_limit_u, ups_limit_v, ups_limit_w). This is always neccesssary for runs with stable stratification, even if this stratification appears only in parts of the model domain.\n\nWith stable stratification the upstream-upline scheme also produces gravity waves with large amplitude, which must be suitably damped (see rayleigh_damping_factor).\n\nImportant: The  upstream-spline scheme is not implemented for humidity and passive scalars (see moisture and passive_scalar) and requires the use of a 2d-domain-decomposition. The last conditions severely restricts code optimization on several machines leading to very long execution times! This scheme is also not allowed for non-cyclic lateral boundary conditions (see bc_lr and bc_ns).\n\nA differing advection scheme can be choosed for the subgrid-scale TKE using parameter use_upstream_for_tke.\n\nstatistic_regions\n\nI 0\n\nNumber of additional user-defined subdomains for which statistical analysis and corresponding output (profiles, time series) shall be made.\n\nBy default, vertical profiles and other statistical quantities are calculated as horizontal and/or volume average of the total model domain. Beyond that, these calculations can also be carried out for subdomains which can be defined using the field rmask within the user-defined software (see chapter 3.5.3). The number of these subdomains is determined with the parameter statistic_regions. Maximum 9 additional subdomains are allowed. The parameter region can be used to assigned names (identifier) to these subdomains which are then used in the headers of the output files and plots.\n\nIf the default NetCDF output format is selected (see parameter data_output_format), data for the total domain and all defined subdomains are output to the same file(s) (DATA_1D_PR_NETCDF, DATA_1D_TS_NETCDF). In case of statistic_regions > 0, data on the file for the different domains can be distinguished by a suffix which is appended to the quantity names. Suffix 0 means data for the total domain, suffix 1 means data for subdomain 1, etc.\n\nIn case of data_output_format = 'profil', individual local files for profiles (PLOT1D_DATA) and time series (PLOTTS_DATA) are created for each subdomain. The individual subdomain files differ by their name (the number of the respective subdomain is attached, e.g. PLOT1D_DATA_1). In this case the names of the files with the data of the total domain are PLOT1D_DATA_0 and PLOTTS_DATA_0. If no subdomains are declared (statistic_regions = 0), the names PLOT1D_DATA and PLOTTS_DATA are used (this must be considered in the respective file connection statements of the mrun configuration file).\n\nsurface_heatflux\n\nR no prescribed\nheatflux\n\nKinematic sensible heat flux at the bottom surface (in K m/s).\n\nIf a value is assigned to this parameter, the internal two-dimensional surface heat flux field shf is initialized with the value of surface_heatflux as bottom (horizontally homogeneous) boundary condition for the temperature equation. This additionally requires that a Neumann condition must be used for the potential temperature (see bc_pt_b), because otherwise the resolved scale may contribute to the surface flux so that a constant value cannot be guaranteed. Also, changes of the surface temperature (see pt_surface_initial_change) are not allowed. The parameter random_heatflux can be used to impose random perturbations on the (homogeneous) surface heat flux field shf\n\nIn case of a non-flat topography, the internal two-dimensional surface heat flux field shf is initialized with the value of surface_heatflux at the bottom surface and wall_heatflux(0) at the topography top face. The parameter random_heatflux can be used to impose random perturbations on this combined surface heat flux field shf\n\nIf no surface heat flux is assigned, shf is calculated at each timestep by u* * theta* (of course only with prandtl_layer switched on). Here, u* and theta* are calculated from the Prandtl law assuming logarithmic wind and temperature profiles between k=0 and k=1. In this case a Dirichlet condition (see bc_pt_b) must be used as bottom boundary condition for the potential temperature.\n\nsurface_pressure\n\nR 1013.25\n\nAtmospheric pressure at the surface (in hPa).\n\nStarting from this surface value, the vertical pressure profile is calculated once at the beginning of the run assuming a neutrally stratified atmosphere. This is needed for converting between the liquid water potential temperature and the potential temperature (see cloud_physics).\n\nsurface_scalarflux\n\nR 0.0\n\nScalar flux at the surface (in kg/(m2 s)).\n\nIf a non-zero value is assigned to this parameter, the respective scalar flux value is used as bottom (horizontally homogeneous) boundary condition for the scalar concentration equation. This additionally requires that a Neumann condition must be used for the scalar concentration (see bc_s_b), because otherwise the resolved scale may contribute to the surface flux so that a constant value cannot be guaranteed. Also, changes of the surface scalar concentration (see s_surface_initial_change) are not allowed.\n\nIf no surface scalar flux is assigned (surface_scalarflux = 0.0), it is calculated at each timestep by u* * s* (of course only with Prandtl layer switched on). Here, s* is calculated from the Prandtl law assuming a logarithmic scalar concentration profile between k=0 and k=1. In this case a Dirichlet condition (see bc_s_b) must be used as bottom boundary condition for the scalar concentration.\n\nsurface_waterflux\n\nR 0.0\n\nKinematic water flux near the surface (in m/s).\n\nIf a non-zero value is assigned to this parameter, the respective water flux value is used as bottom (horizontally homogeneous) boundary condition for the humidity equation. This additionally requires that a Neumann condition must be used for the specific humidity / total water content (see bc_q_b), because otherwise the resolved scale may contribute to the surface flux so that a constant value cannot be guaranteed. Also, changes of the surface humidity (see q_surface_initial_change) are not allowed.\n\nIf no surface water flux is assigned (surface_waterflux = 0.0), it is calculated at each timestep by u* * q* (of course only with Prandtl layer switched on). Here, q* is calculated from the Prandtl law assuming a logarithmic temperature profile between k=0 and k=1. In this case a Dirichlet condition (see bc_q_b) must be used as the bottom boundary condition for the humidity.\n\ns_surface\n\nR 0.0\n\nSurface value of the passive scalar (in kg/m3).\n\nThis parameter assigns the value of the passive scalar s at the surface (k=0). Starting from this value, the initial vertical scalar concentration profile is constructed with s_vertical_gradient and s_vertical_gradient_level.\n\ns_surface_initial\n_change\n\nR 0.0\n\nChange in surface scalar concentration to be made at the beginning of the 3d run (in kg/m3).\n\nIf s_surface_initial_change is set to a non-zero value, the near surface scalar flux is not allowed to be given simultaneously (see surface_scalarflux).\n\nR (10) 10 * 0.0\n\nScalar concentration gradient(s) of the initial scalar concentration profile (in kg/m3 / 100 m).\n\nThe scalar gradient holds starting from the height level defined by s_vertical_gradient_level (precisely: for all uv levels k, where zu(k) > s_vertical_gradient_level, s_init(k) is set: s_init(k) = s_init(k-1) + dzu(k) * s_vertical_gradient) up to the top boundary or up to the next height level defined by s_vertical_gradient_level. A total of 10 different gradients for 11 height intervals (10 intervals if s_vertical_gradient_level(1) = 0.0) can be assigned. The surface scalar value is assigned via s_surface.\n\nExample:\n\nThat defines the scalar concentration to be constant with height up to z = 500.0 m with a value given by s_surface. For 500.0 m < z <= 1000.0 m the scalar gradient is 0.1 kg/m3 / 100 m and for z > 1000.0 m up to the top boundary it is 0.05 kg/m3 / 100 m (it is assumed that the assigned height levels correspond with uv levels).\n\nlevel\n\nR (10)\n\n10 * 0.0\n\nHeight level from which on the scalar gradient defined by s_vertical_gradient is effective (in m).\n\nThe height levels are to be assigned in ascending order. The default values result in a scalar concentration constant with height regardless of the values of s_vertical_gradient (unless the top boundary of the model is higher than 100000.0 m). For the piecewise construction of scalar concentration profiles see s_vertical_gradient.\n\ntimestep_scheme\n\nC * 20\n\n'runge\nkutta-3'\n\nTime step scheme to be used for the integration of the prognostic variables.\n\nThe user can choose between the following schemes:\n\n'runge-kutta-3'\n\nThird order Runge-Kutta scheme.\nThis scheme requires the use of momentum_advec = scalar_advec = 'pw-scheme'. Please refer to the documentation on PALM's time integration schemes (28p., in German) fur further details.\n\n'runge-kutta-2'\n\nSecond order Runge-Kutta scheme.\nFor special features see timestep_scheme = 'runge-kutta-3'.\n\n'leapfrog'\n\nSecond order leapfrog scheme.\nAlthough this scheme requires a constant timestep (because it is centered in time),  is even applied in case of changes in timestep. Therefore, only small changes of the timestep are allowed (see dt). However, an Euler timestep is always used as the first timestep of an initiali run. When using the Bott-Chlond scheme for scalar advection (see scalar_advec), the prognostic equation for potential temperature will be calculated with the Euler scheme, although the leapfrog scheme is switched on.\nThe leapfrog scheme must not be used together with the upstream-spline scheme for calculating the advection (see scalar_advec = 'ups-scheme' and momentum_advec = 'ups-scheme').\n\n'leapfrog+euler'\n\nThe leapfrog scheme is used, but after each change of a timestep an Euler timestep is carried out. Although this method is theoretically correct (because the pure leapfrog method does not allow timestep changes), the divergence of the velocity field (after applying the pressure solver) may be significantly larger than with 'leapfrog'.\n\n'euler'\n\nFirst order Euler scheme.\nThe Euler scheme must be used when treating the advection terms with the upstream-spline scheme (see scalar_advec = 'ups-scheme' and momentum_advec = 'ups-scheme').\n\nA differing timestep scheme can be choosed for the subgrid-scale TKE using parameter use_upstream_for_tke.\ntopography C * 40 'flat'\n\nTopography mode.\n\nThe user can choose between the following modes:\n\n'flat'\n\nFlat surface.\n\n'single_building'\n\nFlow around a single rectangular building mounted on a flat surface.\nThe building size and location can be specified with the parameters building_height, building_length_x, building_length_y, building_wall_left and building_wall_south.\n\nFlow around arbitrary topography.\nThis mode requires the input file TOPOGRAPHY_DATA. This file contains the arbitrary topography height information in m. These data must exactly match the horizontal grid.\n\nAlternatively, the user may add code to the user interface subroutine user_init_grid to allow further topography modes.\n\nAll non-flat topography modes\nrequire the use of momentum_advec = scalar_advec = 'pw-scheme', psolver = 'poisfft' or 'poisfft_hybrid',  alpha_surface = 0.0, bc_lr = bc_ns = 'cyclic'galilei_transformation = .F.cloud_physics  = .F.cloud_droplets = .F.moisture = .F., and prandtl_layer = .T..\n\nNote that an inclined model domain requires the use of topography = 'flat' and a nonzero\nalpha_surface.\n\nug_surface\n\nR\n0.0\nu-component of the geostrophic wind at the surface (in m/s).\n\nThis parameter assigns the value of the u-component of the geostrophic wind (ug) at the surface (k=0). Starting from this value, the initial vertical profile of the\nu-component of the geostrophic wind is constructed with ug_vertical_gradient and ug_vertical_gradient_level. The profile constructed in that way is used for creating the initial vertical velocity profile of the 3d-model. Either it is applied, as it has been specified by the user (initializing_actions = 'set_constant_profiles') or it is used for calculating a stationary boundary layer wind profile (initializing_actions = 'set_1d-model_profiles'). If ug is constant with height (i.e. ug(k)=ug_surface) and  has a large value, it is recommended to use a Galilei-transformation of the coordinate system, if possible (see galilei_transformation), in order to obtain larger time steps.\n\nR(10)\n10 * 0.0\nGradient(s) of the initial profile of the  u-component of the geostrophic wind (in 1/100s).\n\nThe gradient holds starting from the height level defined by ug_vertical_gradient_level (precisely: for all uv levels k where zu(k) > ug_vertical_gradient_level, ug(k) is set: ug(k) = ug(k-1) + dzu(k) * ug_vertical_gradient) up to the top boundary or up to the next height level defined by ug_vertical_gradient_level. A total of 10 different gradients for 11 height intervals (10 intervals  if ug_vertical_gradient_level(1) = 0.0) can be assigned. The surface geostrophic wind is assigned by ug_surface.\n\nR(10)\n10 * 0.0\nHeight level from which on the gradient defined by ug_vertical_gradient is effective (in m).\n\nThe height levels are to be assigned in ascending order. For the piecewise construction of a profile of the u-component of the geostrophic wind component (ug) see ug_vertical_gradient.\n\nups_limit_e\n\nR 0.0\n\nSubgrid-scale turbulent kinetic energy difference used as criterion for applying the upstream scheme when upstream-spline advection is switched on (in m2/s2).\n\nThis variable steers the appropriate treatment of the advection of the subgrid-scale turbulent kinetic energy in case that the uptream-spline scheme is used . For further information see ups_limit_pt\n\nOnly positive values are allowed for ups_limit_e.\n\nups_limit_pt\n\nR 0.0\n\nTemperature difference used as criterion for applying  the upstream scheme when upstream-spline advection  is switched on (in K).\n\nThis criterion is used if the upstream-spline scheme is switched on (see scalar_advec).\nIf, for a given gridpoint, the absolute temperature difference with respect to the upstream grid point is smaller than the value given for ups_limit_pt, the upstream scheme is used for this gridpoint (by default, the upstream-spline scheme is always used). Reason: in case of a very small upstream gradient, the advection should cause only a very small tendency. However, in such situations the upstream-spline scheme may give wrong tendencies at a grid point due to spline overshooting, if simultaneously the downstream gradient is very large. In such cases it may be more reasonable to use the upstream scheme. The numerical diffusion caused by the upstream schme remains small as long as the upstream gradients are small.\n\nThe percentage of grid points for which the upstream scheme is actually used, can be output as a time series with respect to the three directions in space with run parameter data_output_ts = 'splptx', 'splpty', 'splptz'. The percentage of gridpoints  should stay below a certain limit, however, it is not possible to give a general limit, since it depends on the respective flow.\n\nOnly positive values are permitted for ups_limit_pt.\n\nA more effective control of the “overshoots” can be achieved with parameter cut_spline_overshoot.\n\nups_limit_u\n\nR 0.0\n\nVelocity difference (u-component) used as criterion for applying the upstream scheme when upstream-spline advection is switched on (in m/s).\n\nThis variable steers the appropriate treatment of the advection of the u-velocity-component in case that the upstream-spline scheme is used. For further information see ups_limit_pt\n\nOnly positive values are permitted for ups_limit_u.\n\nups_limit_v\n\nR 0.0\n\nVelocity difference (v-component) used as criterion for applying the upstream scheme when upstream-spline advection is switched on (in m/s).\n\nThis variable steers the appropriate treatment of the advection of the v-velocity-component in case that the upstream-spline scheme is used. For further information see ups_limit_pt\n\nOnly positive values are permitted for ups_limit_v.\n\nups_limit_w\n\nR 0.0\n\nVelocity difference (w-component) used as criterion for applying the upstream scheme when upstream-spline advection is switched on (in m/s).\n\nThis variable steers the appropriate treatment of the advection of the w-velocity-component in case that the upstream-spline scheme is used. For further information see ups_limit_pt\n\nOnly positive values are permitted for ups_limit_w.\n\nuse_surface_fluxes\n\nL .F.\n\nParameter to steer the treatment of the subgrid-scale vertical fluxes within the diffusion terms at k=1 (bottom boundary).\n\nBy default, the near-surface subgrid-scale fluxes are parameterized (like in the remaining model domain) using the gradient approach. If use_surface_fluxes = .TRUE., the user-assigned surface fluxes are used instead (see surface_heatflux, surface_waterflux and surface_scalarflux) or the surface fluxes are calculated via the Prandtl layer relation (depends on the bottom boundary conditions, see bc_pt_b, bc_q_b and bc_s_b).\n\nuse_surface_fluxes is automatically set .TRUE., if a Prandtl layer is used (see prandtl_layer).\n\nThe user may prescribe the surface fluxes at the bottom boundary without using a Prandtl layer by setting use_surface_fluxes = .T. and prandtl_layer = .F.. If , in this case, the momentum flux (u*2) should also be prescribed, the user must assign an appropriate value within the user-defined code.\n\nuse_ug_for_galilei_tr\n\nL .T.\n\nSwitch to determine the translation velocity in case that a Galilean transformation is used.\n\nIn case of a Galilean transformation (see galilei_transformation), use_ug_for_galilei_tr = .T.  ensures that the coordinate system is translated with the geostrophic windspeed.\n\nAlternatively, with use_ug_for_galilei_tr = .F., the geostrophic wind can be replaced as translation speed by the (volume) averaged velocity. However, in this case the user must be aware of fast growing gravity waves, so this choice is usually not recommended!\n\nuse_upstream_for_tkeL.F.Parameter to choose the advection/timestep scheme to be used for the subgrid-scale TKE.\n\nBy default, the advection scheme and the timestep scheme to be used for the subgrid-scale TKE are set by the initialization parameters scalar_advec and timestep_scheme, respectively. use_upstream_for_tke = .T. forces the Euler-scheme and the upstream-scheme to be used as timestep scheme and advection scheme, respectively. By these methods, the strong (artificial) near-surface vertical gradients of the subgrid-scale TKE are significantly reduced. This is required when subgrid-scale velocities are used for advection of particles (see particle package parameter use_sgs_for_particles).\n\nvg_surface\n\nR\n0.0\nv-component of the geostrophic wind at the surface (in m/s).\n\nThis parameter assigns the value of the v-component of the geostrophic wind (vg) at the surface (k=0). Starting from this value, the initial vertical profile of the\nv-component of the geostrophic wind is constructed with vg_vertical_gradient and vg_vertical_gradient_level. The profile constructed in that way is used for creating the initial vertical velocity profile of the 3d-model. Either it is applied, as it has been specified by the user (initializing_actions = 'set_constant_profiles') or it is used for calculating a stationary boundary layer wind profile (initializing_actions = 'set_1d-model_profiles'). If vg is constant with height (i.e. vg(k)=vg_surface) and  has a large value, it is recommended to use a Galilei-transformation of the coordinate system, if possible (see galilei_transformation), in order to obtain larger time steps.\n\nR(10)\n10 * 0.0\nGradient(s) of the initial profile of the  v-component of the geostrophic wind (in 1/100s).\n\nThe gradient holds starting from the height level defined by vg_vertical_gradient_level (precisely: for all uv levels k where zu(k) > vg_vertical_gradient_level, vg(k) is set: vg(k) = vg(k-1) + dzu(k) * vg_vertical_gradient) up to the top boundary or up to the next height level defined by vg_vertical_gradient_level. A total of 10 different gradients for 11 height intervals (10 intervals  if vg_vertical_gradient_level(1) = 0.0) can be assigned. The surface geostrophic wind is assigned by vg_surface.\n\nR(10)\n10 * 0.0\nHeight level from which on the gradient defined by vg_vertical_gradient is effective (in m).\n\nThe height levels are to be assigned in ascending order. For the piecewise construction of a profile of the v-component of the geostrophic wind component (vg) see vg_vertical_gradient.\n\nL .T.\n\nParameter to restrict the mixing length in the vicinity of the bottom boundary.\n\nWith wall_adjustment = .TRUE., the mixing length is limited to a maximum of  1.8 * z. This condition typically affects only the first grid points above the bottom boundary.\n\nwall_heatflux R(5) 5 * 0.0 Prescribed kinematic sensible heat flux in W m-2 at the five topography faces:\n\nwall_heatflux(0)    top face\nwall_heatflux(1)    left face\nwall_heatflux(2)    right face\nwall_heatflux(3)    south face\nwall_heatflux(4)    north face\n\nThis parameter applies only in case of a non-flat topography. The parameter random_heatflux can be used to impose random perturbations on the internal two-dimensional surface heat flux field shf that is composed of surface_heatflux at the bottom surface and wall_heatflux(0) at the topography top face.\n\nLast change:  22/08/06 (SR)" ]

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[ "# Number Datatypes\n\nBoth numeric data types (`number` and `slider`) are stored as a number in a DOUBLE column in the database. To set numeric data, a number must be passed to the according setter. The two fields merely differ in their GUI input widgets and the fact that the slider has a min/max value and step size, which the numeric field does not have.\n\n## Numeric", null, "The numeric data field can be configured with a default value. In the GUI it is represented by a spinner field.", null, "## Slider\n\nIn the GUI a slider can be used as a horizontal or vertical widget. It needs to be configured with a min and max value, the increment step and decimal precision.", null, "## Quantity Value\n\nThis is a numeric datatype that also allows to specify a unit.\n\nStart off with defining a global list of known units.", null, "This can also be achieved programmatically.\n\n``````\\$unit = new Pimcore\\Model\\DataObject\\QuantityValue\\Unit();\n\\$unit->setAbbreviation(\"km\"); // mandatory\n\\$unit->setLongname(\"kilometers\");\n\\$unit->setGroup(\"dimension\");\n\\$unit->save();\n``````\n\nIn the class editor, it is possible to restrict the list of valid units on a field-level.", null, "Only those units will be available then.", null, "The following code snippet shows how to set a value.\n\n``````use Pimcore\\Model\\DataObject;\n\n\\$parent = DataObject::getByPath(\"/\");\n\n\\$object = new DataObject\\Test();\n\\$unit = DataObject\\QuantityValue\\Unit::getByAbbreviation(\"km\");\n\\$object->setKey(\"test2\");\n\\$object->setParent(\\$parent);\n\\$object->setHeight(new DataObject\\Data\\QuantityValue(27, \\$unit->getId()));\n\\$object->save();\n``````\n\n### Quantity Value Unit Conversion\n\n#### Static unit conversion\n\nYou can also convert values between units. Therefore you have to define base units, conversion factors and offsets. All units with the same base unit can be converted to each other.\n\nExample: You have physical length units meter (m), millimeters (mm) and inches (\"). Then your quantity value unit configuration could look like:\n\nName Abbreviation Baseunit Factor\nMeter m\nMillimeter mm m 0.001\nInch \" m 0.0254\n\nWhen you now have a quantity value field in your data objects and change the unit to a unit which has the same base unit as the unit before the value gets automatically converted. For example when you have 2 m and change the unit to \"mm\" then the value will automatically change to 2000.\n\nYou can also trigger conversion programmatically:\n\n``````\\$originalValue = new QuantityValue(3, Unit::getByAbbreviation('m')->getId());\n\\$converter = \\$this->container->get(\\Pimcore\\Model\\DataObject\\QuantityValue\\UnitConversionService::class);\n\\$convertedValue = \\$converter->convert(\\$originalValue, Unit::getByAbbreviation('mm'));\n// \\$convertedValue is a QuantityValue with value 3000 and unit mm\n``````\n\nUnits without base unit are expected to be a base unit itself. That is why in above example configuration meter has no base unit - but of course you can set it to meter to be more explicit.\n\nIn quantity value unit configuration there is also the column \"offset\". This is for unit conversions where addition / subtraction is needed. For example\n\nName Abbreviation Baseunit Factor Offset\nDegrees Celcius °C\nDegrees Fahrenheit °F °C 1.8 32\n\nThese conversion parameters result from the formula `°F = °C * 1.8 + 32`\n\n#### Dynamic unit conversion\n\nWhen conversion factors / offsets change over time (e.g. money currencies) or you want to use an external API you have two opportunities:\n\n1. You could periodically update the factors / offsets in quantity value unit configuration\n2. You can create a converter service class\n\nIf you prefer the latter you have to create a class which implements `\\Pimcore\\Model\\DataObject\\QuantityValue\\QuantityValueConverterInterface` and define a service for this class in your `services.yml`. The service name can then be entered in quantity value unit configuration's column \"Converter service\" for the base unit." ]

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[ "Korean J Anesthesiol Search\n\nCLOSE\n\n Korean J Anesthesiol > Volume 72(5); 2019 > Article", null, "In and Lee: Survival analysis: part II – applied clinical data analysis\n\n### Abstract\n\nAs a follow-up to a previous article, this review provides several in-depth concepts regarding a survival analysis. Also, several codes for specific survival analysis are listed to enhance the understanding of such an analysis and to provide an applicable survival analysis method. A proportional hazard assumption is an important concept in survival analysis. Validation of this assumption is crucial for survival analysis. For this purpose, a graphical analysis method and a goodnessof- fit test are introduced along with detailed codes and examples. In the case of a violated proportional hazard assumption, the extended models of a Cox regression are required. Simplified concepts of a stratified Cox proportional hazard model and time-dependent Cox regression are also described. The source code for an actual analysis using an available statistical package with a detailed interpretation of the results can enable the realization of survival analysis with personal data. To enhance the statistical power of survival analysis, an evaluation of the basic assumptions and the interaction between variables and time is important. In doing so, survival analysis can provide reliable scientific results with a high level of confidence.\n\n### Introduction\n\nThe previous article ‘Survival analysis: Part I – analysis of time-to-event’ introduced the basic concepts of a survival analysis . To decrease the gap between the data from a clinical case and a statistical analysis, this article presents several extended forms of the Cox proportional hazards (CPH) model in-series.\nThe most important aspect of the CPH model is a proportional hazard assumption during the observation period. The hazard of an event occurring during an observation cannot always be remained constantly, and the hazard ratio cannot be maintained at a constant level. This is the main obstacle for a clinical data analysis using a CPH model.\nThe basic concepts required to understand and interpret the results of a survival analysis were covered in a previous article . Part 2 of this article, described herein, focuses on the analytical methods applying clinical data and coping with problems that can occur during an analysis. Such methods for validating a proportional hazard assumption apply clinical data and several extended Cox models to overcome the problem of a violated proportional hazard assumption. This article also includes the R codes used for estimating several Cox models based on clinical data. For those familiar with a statistical analysis, the R codes can easily enable an extension of the Cox model estimation.1)\n\n### Proportional Hazard Assumption\n\nRefer to the previous article for a description of diagnostic methods applied to a CPH model. Here, we consider only a proportional hazard assumption. A hazard is defined as the probability of an event occurring at a time point (t). The survival function of a CPH model is an exponential function, and the hazard ratio (λ) is constant during an observation; thus, a survival function is defined in the exponential form of the hazard ratio at a time point (equation 1) .\n##### (1)\ns(t) = expλts(t): survival function based on the CPH modelt: specific time pointλ: hazard ratio\nTo estimate hazard ratio, which is included in the survival function, hazard function (h) is required and it contains a specific explanatory variable (X) which indicates a specific treatment or exposure to a specific circumstance. At the time point of t, the hazard function of the control group is defined as the basal hazard function (h0 (t)), and hazard function of the treatment group as the combined form of the basal hazard function and a certain function with the explanatory variable (X). The hazard ratio is the value of the hazard functions of treatment over control groups (equation 2) .\n##### (2)\nhC (t) = h0 (t)hT (t) = h0 (t) × expβX λ =hT (t)hc (t)=h0 (t) × expβXh0 (t)=expβXhC (t): Hazard function of control grouphT (t): Hazard function of treatment groupλ: Hazard ratioh0 (t): Baseline hazard function at time tt: specific time pointX: explanatory variableβ: coefficient for X\nAs shown in equation 2, the CPH model processes the analysis under the constant hazard ratio assumption with the explanatory variable, which is not affected by the time . The hazard ratio remains constant, and the hazards of each group at any time point remain at a distance and never meet graphically during an observation. However, this does not guarantee the satisfaction of the proportional hazard assumption. In a clinical setting, one hazard could remain lower or higher than the others, and their ratio cannot be constant because the treatment effect may vary owing to various factors. Therefore, we need a statistical method to prove the satisfaction or violation of the proportional hazard assumption.\n\n### Validation of Proportional Hazard Assumption\n\nThere are three representative validation methods of a proportional hazard assumption. One is a graphical approach, another is using the goodness of fit (GOF), and the last is applying a time-dependent covariate [4,5].\n\n### Graphical analysis for validation of proportional hazard assumption\n\nAs mentioned in the previous article, a log minus log plot (LML plot) is one of the most frequently used methods for the validation of a proportional hazard assumption . The log transformation is applied twice during a mathematical process for estimating the survival function. The first log transformation results in negative values because the probability values from the survival function lay between zero and 1, and such values should be made positive to conduct a second log transformation. The name of the LML plot implies this process. A survival function is the exponential form of a hazard ratio, and the hazard ratio is constituted with the hazard function, which is an exponential form of an explanatory variable. As a result of an LML transformation, the survival function is converted into a linear functional form, and the difference from the explanatory variable creates a distance on the y-axis at a time point. Ultimately, survival functions that are log transformed twice become parallel during the observation period. Deductively, two curves on an LML plot also become parallel, which indicates that the hazard ratio remains constant during the observation period .\nThere is a risk of subjective decision regarding the validation of a proportional hazard assumption using an LML plot because this method is based on a visual check. It is recommended that the interpretation be as conservative as possible except under strong evidence of a violation, including instances in which the curves are crossing each other or apparently meet. A continuous explanatory variable should be converted into a categorical variable of two or three levels to produce an LML plot. When doing so, the data thin out and a different result can be reached according to the criteria used for dividing the variable .\n\n### R codes for Kaplan–Meier survival analysis under the assumption of a proportional hazard\n\nThe sample data ‘Survival2_PONV.csv’ contains the imaginary data of 104 patients regarding the first onset time of postoperative nausea and vomiting (PONV). All patients received one of two types of antiemetics (Drugs A or B). The columns represent the patient number (No), types of antiemetics (Antiemetics), age (Age), body weight (Wt), amount of opioid used during anesthesia (Inopioid), the first PONV onset time (Time), and whether PONV occurred (PONV). To load such data into R software 3.5.2 (R Development Core Team, Vienna, Austria, 2018), the following code can be used. In this code, the location of the CSV file on the hard drive is ‘d:’, and users should adequately modify the path. This code provides the first several lines of data (Table 1).\nTRUE, sep = \",\"\n)\n# Check imported data\nTo conduct a survival analysis using R, two R packages are required, ‘survival’2) and ‘survminer’.3) When these packages are not supplied as a default, manual installation is not difficult when using the command ‘install.packages(“package name”)’. These packages are then called.\nlibrary (survival)\nlibrary (survminer)\nThen, a Kaplan–Meier survival analysis is applied. The following code covers a Kaplan–Meier analysis, comparing the PONV using a log-rank test, and the LML plot introduced in part I of this article . Small modifications of this code can enable a survival analysis with the user’s own data.\n### Kaplan-Meier Estimation (KME)\nPONV.raw$Survobj <- with(PONV.raw, Surv(Time, PONV == 1) ) head (PONV.raw) ## Single KME. The log-log confidence interval is preferred. km.one <- survfit(Survobj ~1, data = PONV.raw, conf.type = \"log-log\") # Result of KME km.one # Survival table summary (km.one) # Survival curve ggsurvplot (km.one, data = PONV.raw, conf.int = TRUE, palette = \"grey\", surv.median.line = \"hv\", break.time.by = 4, censor = TRUE, legend = \"none\", xlab = \"Time (hour)\", risk.table = TRUE, tables.height = 0.2, tables.theme = theme_cleantable(), risk.table.y.text = FALSE ) R applies a Kaplan–Meier analysis using the new variable ‘Survobj’. The results of a Kaplan–Meier analysis and a survival table are presented in Table 2. Out of 104 patients, 63 patients suffered from PONV, and the median onset time was 10 h. A graphical presentation is also possible (Fig. 1). Here, ‘ggsurvplot’ produces survival curves with complex arguments, fine-tuning the argument options to draw intuitive graphs. The next code is for an estimation of the survival curves according to two antiemetics and conducting a log-rank test. ### KME by Antiemetics km.antiemetics <- survfit (Survobj ~ Antiemetics, data = PONV.raw, conf.type = \"log-log\" ) # Result of KME by Antiemetics km.antiemetics # Survival table of KME by Antiemetics summary (km.antiemetics) # KM estimation, log-rank test survdiff ( formula = Surv(Time, PONV == 1) ~ Antiemetics, data = PONV.raw ) # Survival curve of KME by Antiemetics ggsurvplot ( km.antiemetics, data = PONV.raw, fun = \"pct\", pval = TRUE, conf.int = TRUE, surv.median.line = \"hv\", linetype = \"strata\", palette = \"grey\", xlab=\"Time (hour)\", legend.title = \"Antiemetics\", legend.labs = c(\"Drug A\", \"Drug B\"), legend = c(.1, .2), break.time.by = 4, risk.table = TRUE, tables.height = 0.2, tables.theme = theme_cleantable(), risk.table.y.text.col = TRUE, risk.table.y.text = TRUE ) Table 3 and Fig. 2 show the results of this code. Antiemetics are coded as 0 for Drug A and 1 for Drug B, namely ‘Antiemetics = 0’ and ‘1’ represent Drugs A and B, respectively in the Table and Figure. As the interpretation of a log-rank test, the survival functions of two antiemetics are statistically different (P = 0.009), and the median PONV free time is 13 and 6 h for Drugs A and B, respectively. The log-rank test is also based on the proportional hazard assumption, and an LML plot can be used to validate this assumption. The code for this process is as follows, and the output graph is shown in Fig. 3.4,5) # LML plot plot (survfit(Surv(Time, PONV == 1) ~ Antiemetics, data = PONV.raw), fun = \"cloglog\") ### The goodness of fir test (GOF test) The second method for validating a proportional hazard assumption is a GOF test between the observed and estimated survival function values. This provides a P value and hence is a more objective method than a visual check . A Schoenfeld residual test is a representative GOF test for validation of a proportional hazard assumption . A Schoenfeld residual is the difference between explanatory variables observed in the real world and estimated using a CPH model for patients who experience an event. Thus, Schoenfeld residuals are calculated using all explanatory variables included in the model. If the CPH model includes two explanatory variables, the two Schoenfeld residuals come out for one patient at a time.6) Because the hazard ratio is constant during the observation period (a proportional hazard assumption), Schoenfeld residuals are independent of time. A violation of the proportional hazard assumption may be suspected when the Schoenfeld residual plot presents a relationship with time. Also, a Schoenfeld residual test is possible under a null hypothesis of ‘there is no correlation between the Schoenfeld residuals and ranked event time’.7) Schoenfeld residual tests cannot be used to validate a proportional hazard assumption in a Kaplan–Meier estimation because it is based on estimated values using the CPH model. A Schoenfeld residual test is lacking in terms of the statistical hypothesis testing process. Null hypothesis significance testing applies a statistical process to validate ‘no difference,’ and when the null hypothesis is not true under a significant level, an alternative hypothesis is true except for the probability of the significance level, that is, differences exist between comparatives within the probability of significance. A Schoenfeld residual test determines whether a proportional hazard assumption is violated based on the probability of the correlation statistics. Correlation statistics with a higher probability than the significance level result in a satisfaction of the proportional hazard assumption without null hypothesis testing. This method cannot guarantee sufficient evidence to reject a hypothesis, however. Furthermore, the P value is dependent on the sample size, and large sample size will produce a high significance with a minimal violation of the assumption; an apparent assumption violation may be insignificant with small sample size. Although a Schoenfeld residual test is more objective than an LML plot, the use of two methods simultaneously is recommended owing to the problems listed above [4,5,7]. ### R codes for the Cox proportional hazard regression model and GOF test To estimate a CPH model, libraries used in a Kaplan–Meier analysis are also required. After importing the data and calling the required libraries, the CPH model can be estimated according to the antiemetics using the following code. # Univariate Cox proportional hazard model # for a single covariate cph.antiemetics <- coxph(Surv(Time, PONV == 1) ~ Antiemetics , data = PONV.raw ) summary(cph.antiemetics) Table 4 summarizes the results. The PONV incidence rate is 1.9471-fold higher (95% CI, 1.174–3.229, P = 0.010) in the drug B groups than in the drug A groups. Survival2_PONV.csv has four covariates. A multivariate analysis is possible using these covariates with a CPH model. Multivariate analysis can estimate the most compatible model, including significant covariates, through regression diagnostic statistics. Still, several controversies remain , both directional stepwise selection methods are applied in this example. # Multivariate Cox regression cph.full <- coxph (Surv(Time, PONV == 1) ~ Antiemetics + Age + Wt + Inopioid , data = PONV.raw ) summary (cph.full) # Variables selection cph.selection <- step( coxph(Surv(Time, PONV == 1) ~ Antiemetics + Age + Wt + Inopioid , data = PONV.raw) , direction = \"both\" ) summary (cph.selection) # Final model selected cph.selected <- coxph(Surv(Time, PONV == 1) ~ Antiemetics + Inopioid , data = PONV.raw ) summary (cph.selected) After examining the full model including all covariates (summary(cph.full)), the most compatible model is confirmed through a covariate selection (summary(cph.selection)), and a clean result is finally obtained (summary(cph.selected)). Table 5 shows the final model. According to the result, the PONV increment is estimated as 2.021-fold (95% CI, 1.217–3.358, P = 0.007) based on the antiemetics, and 1.013-fold (95% CI, 1.008–1.018, P < 0.001) based on intraoperative opioid usage. The next code draws survival curves against the antiemetics for the final model (Fig. 4).8) # Survival curves of the Cox PH model # grouped by Antiemetics new.cph.antiemetics <-with (PONV.raw ,data.frame(Antiemetics = c(0, 1), Inopioid = c(0,0) )) new.cph.antiemetics.fit <- survfit(cph.selected , newdata = new.cph.antiemetics ) ggsurvplot(new.cph.antiemetics.fit , data = PONV.raw , conf.int = TRUE , conf.int.style = \"step\" , censor = FALSE , palette = \"grey\" , break.time.by = 4 , linetype = \"solid\" , axes.offset = FALSE , xlab = \"Time (hour)\" , legend = c(0.1, 0.15) , legend.labs = c(\"Drug A\", \"Drug B\") , legend.title = \"Antiemetics\") The R code for an LML plot is described above. For categorical variables, an LML plot provides an easy to interpret and intuitive validation method for a proportional hazard assumption.9) Validation of the proportional hazard assumption of the antiemetics, which is a categorical variable, is possible using an LML plot. (Fig. 5) #LML for CoxPH plot (survfit(coxph(Surv(Time, PONV == 1) ~ strata(Antiemetics) , data = PONV.raw ) ), fun = \"cloglog\" ) The proportional hazard assumption of the antiemetics is not violated according to the graphs shown in Fig. 5. The covariate “Inopioid” is a continuous type of variable, and an LML plot using this variable is impossible to achieve without a categorical transformation. A Schoenfeld residual test is shown below. Here, ‘cox.zph’ included in the ‘survminer’ library enables this test. The results are listed in Table 6, and graphical output is shown in Fig. 6. # Schoenfeld residuals test sf.residual <- cox.zph(cph.selected) print(sf.residual) # display the results par (mfrow = c(2,1)) plot(sf.residual) # plot curves abline (h = coef(cph.selected) , lty = \"dotted\", lwd = 1) plot(sf.residual) abline (h = coef(cph.selected) , lty = \"dotted\", lwd = 1) The P value in Table 6 indicates the significance probability of the Schoenfeld residual test for the antiemetics and intraoperative opioid used, and such values indicate a violation of the proportional hazard assumption. A positive increment of the Schoenfeld residual curve for ‘Inopioid’ is shown in Fig. 6. The curve for the antiemetics gradually changes toward a negative value over time, but not continuously. In this way, a Schoenfeld residual test provides more objective results than an LML plot, which is strictly conservative. ### Adding a time-dependent covariate To validate a proportional hazard assumption in a CPH model, a time-dependent covariate is intentionally added into the estimated model. This covariate can be made using a time-independent variable and time, or a function of time. For example, the process compares two models, namely, a CPH model that assumes the proportional hazard assumption has not been violated, and another model incorporated with a combined covariate of the explanatory variable and time (or a function of time) in the estimated CPH model. A likelihood ratio test or Wald statistics are used for comparison. This type of method has certain advantages, including a simultaneous comparison with multiple covariates and various time functions; note that the results may change depending on the covariates and types of functions selected [5,10,11].10) ### Cox Proportional Hazard Regression Models with Time-dependent Covariates Covariates violating the proportional hazard assumption in a CPH model should be adequately adjusted. This section introduces a stratification and time-dependent Cox regression to deal with covariates violating the proportional hazard assumption. ### Stratified Cox proportional hazard model To fit the CPH model with variables violating the proportional hazard assumption, one method is to apply a stratified CPH model. This method makes one integrated result from the results of each stratum containing a categorical variable classified based on a certain criterion. Unlike the Mantel–Haenszel method, which is based on the sample size of each stratum, stratification in the CPH model sets a different baseline hazard corresponding to each stratum, and a statistical estimation is then applied to achieve common coefficients for the remaining explanatory variables except for the stratified variables.11) This provides a hazard ratio of the controlled effects of variables violating the proportional hazard assumption . A stratified CPH model can be applied to control the variables violating a constant hazard assumption, as well as to control the confounding factors that influence the results with little or no clinical significance. Stratification always requires categorical variables, and conversion into categorical variables is required for continuous variables. Under this situation, care should be taken that the sample size of each stratum is reduced (data thinned out) and information held by the continuous variable is simplified. Therefore, conversion into a categorical variable should consider as small number of strata as possible, setting the range of clinical or scientific meaning, and maintaining a balance among the strata . ### R codes for stratified Cox proportional hazard model In the previous CPH modeling, the variable ‘Inopioid’ violated the constant hazard assumption based on the Schoenfeld residual test (Fig. 6). Here, ‘Inopioid’ is a continuous variable that records the dose of intraoperatively used opioid. To apply a stratified CPH modeling, continuous variables should be converted into categorical variables. For convenience, the following is a code that converts ‘Inopioid’ into a categorical variable of 0 or 1, when not used or used, respectively. ##### Stratified Cox regression ### Add categorical variables from Inopioid PONV.raw <- transform(PONV.raw, Inopioid_c = ifelse( Inopioid == 0, 0, 1)) head (PONV.raw) According to this, the categorical variable ‘Inopioid_c’ is recorded as 0 or 1 and is newly added to the dataset (Table 7). Next, the code for a stratified CPH model is as follows: ### Stratified Cox proportional hazard modeling cph.strata <- coxph (Surv(Time, PONV == 1) ~ Antiemetics + strata(Inopioid_c) , data = PONV.raw) summary (cph.strata) ggsurvplot(survfit(cph.strata) , data = PONV.raw , risk.table = TRUE , palette = c(\"black\",\"black\") , linetype = c(\"solid\",\"dashed\") ) par( mfrow = c(1,1)) plot (survfit(cph.strata) , fun = \"cloglog\" , main = \"Antiememtics\" ) sf.residual.strata <- cox.zph(cph.strata) print(sf.residual.strata) plot(sf.residual.strata) abline (h = coef(cph.strata) , lty = \"dotted\" , lwd = 1) This code outputs a stratified CPH model by controlling ‘Inopioid_c’ (Table 8). The command ‘ggsurvplot’ provides survival curves of two strata and prints the LML plot using the last ‘plot’ command (Fig. 7). The Schoenfeld residual test using a ‘cox.zph’ command reveals that ‘Antiemetics’ violates the proportional hazard assumption (rho = −0.265, chisq = 4.26, P = 0.039, shown in Fig. 8). It is possible to obtain an adequate CPH model by stratifying ‘Inopioid’ and ‘Antiemetics’, although the interpretations may be complex because it is difficult to integrate the comparison results among all strata. ### Time-dependent Cox regression Most clinical situations change over time, and the variables affected by a specific treatment also change even when the treatment remains constant during the observation period . For example, consider an analgesic having a toxic effect on the hepatobiliary function for patients with chronic pain. A periodic liver function test will be crucial, and all laboratory results will vary for every follow-up time. The administration dose may also vary according to the laboratory results or analgesic effects. Moreover, the laboratory results may not be valid after the patients are censored or after an event occurs. These variables are common in clinical practice, and the existence of time-dependent variables should be considered and checked before starting the data collection for survival analysis. If an adequate measurement method is developed, a time-dependent covariate Cox regression will be possible. Another type of time-dependent variable is a covariate with a time-dependent coefficient . If the analgesics mentioned above produces a level of tolerance, its effect decreases over time. This indicates that the risk of breakthrough pain occurrence may be higher as time passes, which apparently violates the proportional hazard assumption. In this case, the effect of the analgesics can be included in the survival function, which is expressed as a covariate with a coefficient of the function of time. As mentioned above, a time-dependent covariate is incorporated into the analysis as a single value according to the repeated observation intervals. For example, a patient under analgesics medication takes an initial liver function test, the results of which show 40 IU/L and 100 IU/L after four weeks with continued pain and 130 IU/L at eight weeks with pain, whereas at 12 weeks after analgesics administration, the pain is subsided and medications are discontinued without a further laboratory test. The laboratory data input for the time-dependent covariate are 40 until 4th weeks without an event, 100 from 4th to 8th weeks without an event, 130 from 8th to 12th weeks, and an event occurs at 12th weeks. Clinical studies in the area of anesthesiology often include variables related to the response or effect of a specific treatment or medication. Depending on the characteristics and measurement methods of the variables, once a specific treatment or medication is applied, their effects are gradually decreased over time or delayed until the onset time. The effects of treatment or medication changes over time, the coefficient of these effects can be expressed as a time function, and for Cox regression, a step function is frequently applied. A step function is a method applying different coefficient values to different time intervals. A Cox regression can thus be established and output the integrated results . In addition, a continuous parametric function for a time-dependent coefficient can be used for analysis instead of a step function . ### R code for time-dependent coefficient Cox regression model: step function As shown in Fig. 6, the Schoenfeld residuals of ‘Antiemetics’ and ‘Inopioid’ turn from positive to negative or vice versa at approximately 3 and 6 h. The data are arbitrarily separated using these time points. tdc <- survSplit (Surv(Time, PONV) ~. , data = PONV.raw , cut=c(3, 6) , episode = \"tgroup\" , id = \"id\" ) head(tdc) The command ‘survSplit’ separates the patient data according to the established time interval, where the value for each interval is the measured value on the left side of the interval (start time, ‘tstart’), and ‘Time,’ which is the end of the interval succeeds the next interval. That is, one interval is closed at the left and opened at the right, and if an event occurs during the interval, the survival function is estimated using the variables measured at the left side of the interval (Table 9). It seems that the data being duplicated at the end and the start of the interval, problems do not occur because the divided time does not overlap. It is possible to apply a Cox regression and GOF test with these separated data. # Fitting Cox regression fit.tdc <- coxph(Surv(tstart,Time, PONV) ~ Antiemetics:strata(tgroup) + Inopioid , data = tdc) summary(fit.tdc) # GOF test sf.tdc <- cox.zph(fit.tdc) print (sf.tdc) par(mfrow=c(2,2)) plot(sf.tdc) abline (h = coef(fit.tdc), lty = \"dotted\") plot(sf.tdc) abline (h = coef(fit.tdc), lty = \"dotted\") plot(sf.tdc) abline (h = coef(fit.tdc), lty = \"dotted\") plot(sf.tdc) abline (h = coef(fit.tdc), lty = \"dotted\") Table 10 shows the estimated Cox regression and GOF test results, and Fig. 9 presents a plot of the Schoenfeld residuals. The risk of the PONV increases 1.0126-fold (95% CI: 1.0078–1.017, P < 0.001) by one unit of intraoperative opioid. For the antiemetics, the group taking drug B showed an increased PONV risk of 3.6545-fold (95% CI: 1.2024–11.107, P = 0.022) until 3 h post-operation, 3.8969-fold (95% CI: 1.4020–10.831, P = 0.009) until 6 h post-operation, with no significant difference shown until the end of the observation (risk ratio = 0.9382, 95% CI: 0.4242–2.075, P = 0.957). The results of the Schoenfeld residual test (Table 10 and Fig. 9) indicate that all variables do not violate the proportional hazard assumption. These results cannot provide a single desired outcome, and it is necessary to combine the results. # Combined results combine.tdc <- data.frame(tstart = rep(c(0,3,6), 2) , Time = rep(c(3,6, 24), 2) , PONV = rep(0,12) , tgroup= rep(1:3,4) , trt = rep(1,12) , prior= rep(0,12) , Antiemetics = rep(c(0,1), each = 6) , Inopioid = rep (c(0,1), each = 3) , parameter = rep(0:1, each = 6) ) combine.tdc cfit.tdc <- survfit(fit.tdc , newdata = combine.tdc , id = parameter ) cfit.tdc km <- survfit(Surv(Time, PONV) ~Antiemetics , data = PONV.raw ) summary (km) km par( mfrow = c(1,1)) plot(km, xmax= 24, col=\"Black\" , lty = c(\"solid\",\"dashed\"), lwd=2 , xlab=\"Postoperative hours\" , ylab=\"PONV free\" ) lines(cfit.tdc, col=\"Grey\" , lty= c(\"solid\",\"dashed\"), lwd=2) legend (x = 0.15, y = 0.25 , c(\"Drug A, Kaplan-Meier estimation\" , \"Drug B, Kaplan-Meier estimation\" , \"Drug A, Cox regression with time-dependent coefficient\" , \"Drug B, Cox regression with time-dependent coefficient\" ) , col = c(\"black\", \"black\", \"grey\", \"grey\") , lty = c(\"solid\", \"dashed\", \"solid\", \"dashed\") ) To compare the results from two antiemetics, the data divided by ‘survSplit’ are combined to enable an interpretation (combine. tdc). The results are shown in Table 11. The survival model considering the time-dependent coefficient increases the sample size because the data of one patient are separated at the established time points. Note that the median survival times in this model are 31 and 16 h, and the median survival times from the Kaplan–Meier analysis are 13 and 6 h. Plotting these two models into a single graph enables a visual comparison (Fig. 10). Here, although ‘ggsurvplot’ provides comprehensive graphs, it cannot draw two graphs simultaneously. Another graphics software is required to make a single graph from these graphs (Fig. 11). ## plot using ggsurvplot ggsurvplot ( km, data = PONV.raw, fun = \"pct\", pval = TRUE, conf.int = TRUE, surv.median.line = \"hv\", linetype = \"strata\", palette = \"grey\", legend.title = \"Antiemetics\", legend.labs = c(\"Drug A\", \"Drug B\"), legend = c(.1, .2), break.time.by = 4, xlab = \"Time (hour)\", risk.table = TRUE, tables.height = 0.2, tables.theme = theme_cleantable(), risk.table.y.text.col = TRUE, risk.table.y.text = TRUE ) ggsurvplot ( cfit.tdc, data = PONV.raw, fun = \"pct\", conf.int = TRUE, surv.median.line = \"hv\", linetype = \"strata\", palette = \"grey\", legend.title = \"Antiemetics\", legend.labs = c(\"Drug A\", \"Drug B\"), legend = c(.1, .2), break.time.by = 4, xlab = \"Time (hour)\", risk.table = TRUE, tables.height = 0.2, tables.theme = theme_cleantable(), risk.table.y.text.col = TRUE, risk.table.y.text = TRUE ### Conclusions Clinical studies in the area of anesthesiology had rarely presented statistical results using survival analysis. In recent years, studies on the survival or recurrence of cancer according to the anesthetics have been actively published . Survival analysis has the power to present clear and comprehensive results based on studies on pain control or the effects of medications. Previous articles have focused on the basic concepts of survival analysis and interpretations of the published results , and the present article covered the process of conducting a survival analysis using clinical data, finding errors, and achieving adequate results. Although this article does not include all existing survival analysis methods, it introduced several R codes to enable an intermediate level of survival analysis for clinical data in the field of anesthesiology.12) Some clinical papers dealing with a survival analysis have presented statistical results without considering a proportional hazard assumption or an interaction between the covariates and time. The power of a log-rank test, which is commonly used to compare two groups, tends to decrease when a proportional hazard assumption is violated and can generate an incorrect result [19,20]. An investigation into the reporting of survival analysis results in leading medical journals indicated that the use of survival analysis has significantly increased, although several problems still exist, including descriptions regarding the censoring, sample size calculation, constant proportional hazard ratio assumption validations, and GOF testing . Because most statistical analyses require several basic assumptions, survival analysis also requires some essential assumptions. In a Kaplan–Meier analysis, the likelihood of an event of interest and censoring occurring should be independent from each other, and the survival probabilities of patients who participated in earlier and later studies should be similar. A log-rank test also requires the previously described and proportional hazard assumptions . A CPH model requires a proportional hazard assumption, independence between the survival times among different patients, and a multiplicative relationship between the predictors and hazard . When reporting or interpreting the results of survival analysis, it is important that the identification of the underlying assumptions corresponds to the statistical analysis, and it is necessary to verify that the assumptions are reasonable and well maintained. Statistical results with violated assumptions cause deviated decisions because of an increased probability of error. Survival analysis will be a powerful tool to achieve a scientific conclusion when an appropriate method is chosen with regard to the nature of the variables, the relationship with time, and other basic assumptions. ### NOTES 1) Sample data (Survival2_PONV.csv) and the R console output of entire code are provided as supplemental information. Refer to online help or R statistical textbooks for detailed explanations of the argument. The included R code covers the process beginning with the survival analysis introduced in . A detailed description of a violation of a proportional hazard assumption is provided in . 2) Terry M. survival: Survival Analysis. R package version 2.42-4. 2018. https://github.com/therneau/survival. 3) Alboukadel K, Marcin K, Przemyslaw B, Scheipl F. survminer: Drawing Survival Curves using 'ggplot2', R package version 0.4.3. 2018. http://www.sthda.com/english/rpkgs/survminer/. 4) There are several ways to draw an LML plot in R; ‘plot.survfit’ with the argument ‘fun = “cloglog”’ provides an LML plot of the log-scaled x-axis. Most statistical references describe a log-scaled x-axis LML plot, whereas others describe a standard linear-scaled x-axis LML plot. The R code for a non-log-scaled LML plot can be created through the following. # Non-log scaled LML plot ponvsurv=Surv(PONV.raw$Time, PONV.raw$PONV) NLML.fun=function(p){return(log(-log(p)))} plot (survfit(ponvsurv ~ PONV.raw$Antiemetics), fun=NLML.fun)\n\n5) R package ‘survival’ version 2.44-1 (updated in March 2019) has an error with an x value of 1 when log scaled using the x-axis. Versions before 2.44-1 work properly.\n\n6) Schoenfeld residual is only for the patient who experienced the event. It is the difference between observed value of explanatory variable at a specific time and expected value of the explanatory variable (covariate) at a specific time which is a weighted-average value by likelihood of event from the risk set at that time point.\n\n7) Some statistical software provides a method using scaled Schoenfeld residuals. Under a specific circumstance, these two results are different, although they mostly produce similar results. Please refer to the following: Grambsch, P.M. and Therneau, T.M. 1994. Proportional hazards tests and diagnostics based on weighted residuals. Biometrika 81: 515-526.\n\n8) The command ‘ggadjustedcurves’ included in the ‘survminer’ library easily produces the survival curves of the CPH model. Unfortunately, this command still has minor functional errors such as in printing the 95% CI or labelling, and a somewhat complex ‘ggsurvplot’ is used in this example.\n\n9) In R, categorical variables should be treated as a stratum for comparison using an LML plot of the CPH model.\n\n10) Because various application methods and their variations are available, they are not discussed in detail herein.\n\n11) This is a non-interaction stratified CPH model. Several survival functions are estimated through stratification, and if the explanatory variables have interactions with each other, the coefficients at each stratum may be different. In this case, it is assumed that an interaction model between explanatory variables and a likelihood ratio test provide clues to judge whether there is an interaction between explanatory variables. That is, if two or more variables are included in the model, it is necessary to check whether an interaction between them exists.\n\n12) A clustered event time analysis and an accelerated failure time analysis are often applied to survival analysis methods in clinical study. A clustered event time analysis is similar with a stratified CPH model, and has certain advantages when each stratum has insufficient event cases. It has two types of processes, one is a marginal approach that estimates the survival function through an overall cluster from the pooled effect of each stratum, and another is a conditional approach that estimates the survival function from the heterogeneity between clusters. An accelerated failure time analysis estimates the model similarly with a linear regression based on a Weibull distribution or log-logistic distribution. Unlike a CPH model that continuously maintains the risk ratio of the covariates, this model assumes that the disease process can be accelerated or decelerated over time.\n\n### NOTES\n\nConflicts of Interest\n\nAuthor Contributions\n\nJunyong In (Conceptualization; Writing–original draft; Writing–review & editing)\n\nDDong Kyu Lee (Conceptualization; Writing–original draft; Writing – review & editing)\n\n### Supplementary Materials\n\nFuther detailes are presented in the online version of this article (Available from https://doi.org/10.4097/kja.19183).\n##### Fig. 1.\nKaplan–Meier curve of overall survival status with sample data. A 95% confidence interval (estimated from a log hazard) is presented in the shadowed area. The dashed line indicates the median survival time.", null, "##### Fig. 2.\nKaplan–Meier curves of two antiemetics with sample data. The P value is estimated based on a log-rank test. A 95% confidence interval (estimated from a log hazard) is presented in the shadowed area. The dashed lines indicate the median survival times of groups taking Drugs A and B. Drug A is coded as ‘Antiemetics = 0’ and Drug B is coded as ‘Antiemetics = 1’ in the original data.", null, "##### Fig. 3.\nLog minus log plot of Kaplan–Meier estimation with log-rank test between two antiemetics. The two curves do not meet during the observation period, indicating the satisfaction of the proportional hazard assumption. The log-time scale is shown in the x-axis.", null, "##### Fig. 4.\nSurvival curves of antiemetics estimated using the Cox proportional hazards regression model. a solid black line indicates Drug A (Antiemetics = 0) and a solid grey line indicates Drug B (Antiemetic = 1). Dashed lines present a 95% CI range. Drug A is coded as ‘Antiemetics = 0’ and drug B is coded as ‘Antiemetics = 1’ in the original data.", null, "##### Fig. 5.\nLML plot of Cox proportional hazards model based on antiemetics with sample data.", null, "##### Fig. 6.\nSchoenfeld residual plot with ‘Antiemetics’ and ‘Inopioid’. Dotted horizontal lines indicate the estimated coefficient values of these covariates.", null, "##### Fig. 7.\nExamples of the stratified Cox proportional hazard model and corresponding LML plot. (A) Survival curves of estimated stratified Cox proportional hazard model. Stratification is achieved using the categorical variable ‘Inopioid_c’. (B) Log-minus log plot for evaluation of proportional hazard assumption against two antiemetics. Note that a non-parallelism of below 2 h is not assured, whereas the overall curves are roughly parallel without crossing.", null, "##### Fig. 8.\nSchoenfeld residual test for the stratified Cox proportional hazard model. For the covariate ‘Antemetics’, the probability was estimated as 0.039, and a violation of the proportional hazard assumption was strongly suggested under the controlled covariate ‘Inopioid’ (the dotted horizontal line shows the estimated coefficient of ‘Antiemetics’).", null, "##### Fig. 9.\nSchoenfeld residual graphs of time-dependent coefficient Cox regression.", null, "##### Fig. 10.\nGraphical comparison between survival models of Kaplan– Meier and Cox regression with time-dependent coefficient. Black curves indicate the model fitted using a Kaplan–Meier analysis, and the gray curves are from a Cox regression with a time-dependent coefficient. The solid lines indicate Antiemetics = 0 (Drug A), and the dashed lines indicate Antiemetics = 1 (Drug B).", null, "##### Fig. 11.\nCox regression model with the time-dependent coefficient. Survival curves of Kaplan–Meier analysis (A) and time-dependent coefficient (B) using ‘ggsurvplot’ command. Gray solid lines indicate Antiemetics = 0 (Drug A), and the black dashed lines indicate Antiemetics = 1 (Drug B). The results of the survival analysis are changed when considering the constant hazard ratio assumption.", null, "##### Table 1.\nFirst Three Data Imported as PONV.raw\nNo Antiemetics Age Wt Inopioid Time PONV\n1 1 0 48 78.5 0 4 0\n2 3 0 54 88.3 100 21 0\n3 4 0 22 49.4 0 14 0\n\nFrom the left, each column contains each coded variable: The first column has a number automatically generated by R, variable ‘No’ is a coded number in the original data, ‘Antiemetics’ has a value of 0 for Drug A and 1 for Drug B, ‘Age’ and ‘Wt’ are the actual patients’ age and body weight, ‘Inopioid’ is the amount of opioid used during surgery, ‘Time’ indicates the onset time of postoperative nausea and vomiting (PONV), and ‘PONV’ is coded as 1 when the patient experienced PONV.\n\n##### Table 2.\nResults of Kaplan–Meier Estimation and Survival Table\nCall: survfit(formula = Survobj ~ 1, data = PONV.raw, conf.type = \"log − log\")\nn Events Median 0.95LCL 0.95UCL\n104 63 10 7 16\n\nCall: survfit(formula = Survobj ~ 1, data = PONV.raw, conf.type = \"log − log\")\nTime n.risk n.event Survival std.err Lower 95% CI Upper 95% CI\n\n1 104 8 0.923 0.0261 0.852 0.961\n2 96 7 0.856 0.0345 0.772 0.910\n3 89 3 0.827 0.0371 0.739 0.887\n\nn: total number of cases, Events: number of patients who experienced PONV, Median: median survival time, 0.95LCL: lower limit of 95% confidence interval, 0.95UCL: upper limit of 95% confidence interval, n.risk: number at risk, n.event: number of event, Survival: survival rate, std.err: standard error of survival rate, Lower/upper 95% CI: lower/upper limits of 95% confidence interval.\n\n##### Table 3.\nResults of Kaplan–Meier Estimation between Antiemetics, Survival Tables of Two Antiemetics, and Comparison Results of Log-rank Test\nCall: survfit(formula = Survobj ~ Antiemetics, data = PONV.raw, conf.type = \"log − log\")\nn Events Median 0.95LCL 0.95UCL\nAntiemetics = 0 51 25 13 9 NA\nAntiemetics = 1 53 38 6 4 10\n\nCall: survfit(formula = Survobj ~ Antiemetics, data = PONV.raw, conf.type = \"log − log\")\nAntiemetics = 0\nTime n.risk n.event Survival std.err Lower 95% CI Upper 95% CI\n\n1 51 1 0.980 0.0194 0.869 0.997\n2 50 2 0.941 0.0329 0.829 0.981\n3 48 1 0.922 0.0376 0.804 0.970\n4 47 2 0.882 0.0451 0.757 0.945\n\nAntiemetics = 1\nTime n.risk n.event Survival std.err Lower 95% CI Upper 95% CI\n\n1 53 7 0.868 0.0465 0.743 0.935\n2 46 5 0.774 0.0575 0.636 0.865\n3 41 2 0.736 0.0606 0.595 0.834\n4 39 6 0.623 0.0666 0.478 0.738\n\nCall: survdiff(formula = Surv(Time, PONV == 1) ~ Antiemetics, data = PONV.raw)\nN Observed Expected\n\nAntiemetics = 0 51 25 34.9\nAntiemetics = 1 53 38 28.1\nChisq = 6.8 on 1 degrees of freedom, P = 0.009\n\nAntiemetics = 0 and 1 indicate Drugs A and B, respectively. Because the variable ‘Antiemetics’ is coded as 0 for drug A and 1 for drug B, the R output only describes these as ‘Antiemetics = 0 and 1’. n: total number of cases, Events: number of patients who experienced postoperative nausea and vomiting, Median: Median survival time, 0.95LCL: lower limit of 95% confidence interval, 0.95UCL: upper limit of 95% confidence interval, n.risk: number at risk, n.event: number of events, Survival: survival rate, std.err: standard error of survival rate, Lower/upper 95% CI: lower/upper limits of 95% confidence interval, Chisq: chi-squared statistics.\n\n##### Table 4.\nResults of the Cox Proportional Hazard Model Estimation Using Antiemetics with Sample Data\nCall: coxph(formula = Surv(Time, PONV == 1) ~ Antiemetics, data = PONV.raw)\nn = 104, number of events = 63\ncoef exp(coef) se(coef) z Pr(>|z|)\nAntiemetics 0.6664 1.9471 0.2581 2.582 0.00983**\n---\n\nSignif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘’ 1\nexp(coef) exp(-coef) Lower .95 Upper .95\n\nAntiemetics 1.947 0.5136 1.174 3.229\nConcordance = 0.615 (se = 0.032)\nRsquare = 0.064 (max possible = 0.993)\nLikelihood ratio test = 6.85 on 1 df, P = 0.009\nWald test = 6.67 on 1 df, P = 0.01\nScore (logrank) test = 6.91 on 1 df, P = 0.009\n\n‘Antiemetics’ is coded as 0 for Drug A or 1 for Drug B in the original data. coef: the value of coefficient, exp(coef): exponential value of coefficient, se(coef): standard error of coefficient, z: z-statistics, Pr(>|z|): P value of given z-statistics, Signif. codes: codes for significance marking.\n\n##### Table 5.\nMultivariate Cox Proportional Hazard Model with Sample Data\nCall: coxph(formula = Surv(Time, PONV == 1) ~ Antiemetics + Inopioid, data = PONV.raw)\nn = 104, number of events = 63\ncoef exp(coef) se(coef) z Pr(>|z|)\nAntiemetics 0.703650 2.021116 0.258971 2.717 0.00659**\nInopioid 0.012740 1.012821 0.002417 5.271 1.35e-07***\n---\n\nSignif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘’\nexp(coef) exp(-coef) Lower .95 Upper .95\n\nAntiemetics 2.021 0.4948 1.217 3.358\nInopioid 1.013 0.9873 1.008 1.018\nConcordance = 0.694 (se = 0.03)\nRsquare = 0.284 (max possible= 0.993)\nLikelihood ratio test = 34.69 on 2 df, P = 3e-08\nWald test = 34.09 on 2 df, P = 4e-08\nScore (logrank) test = 38.29 on 2 df, P = 5e-09\n\n‘Antiemetics’ is coded as 0 for Drug A or 1 for Drug B in the original data. ‘Inopioid’ is the amount of opioid used during surgery. coef: the value of coefficient, exp(coef): exponential value of coefficient, se(coef): standard error of coefficient, z: z-statistics, Pr(>|z|): P value of given z-statistics, Signif. codes: codes for significance marking.\n\n##### Table 6.\nResults of the Schoenfeld Residual Test\nResults of ‘print(sf.residual)’\nrho chisq P\nAntiemetics −0.275 4.5 0.0340\nInopioid 0.307 5.36 0.0206\nGLOBAL NA 10.26 0.0059\n\n‘Antiemetics’ is coded as 0 for Drug A or 1 for Drug B in the original data. ‘Inopioid’ is the amount of opioid used during surgery. rho: Spearman’s ρ statistics, chisq: chi-squared statistics, P: P value.\n\n##### Table 7.\nPONV.raw Added a New Categorical Variable ‘Inopioid_c’ from the Variable ‘Inopioid’\nNo Antiemetics Age Wt Inopioid Time PONV Survobj Inopioid_c\n1 1 0 48 78.5 0 4 0 4+ 0\n2 3 0 54 88.3 100 21 0 21+ 1\n3 4 0 22 49.4 0 14 0 14+ 0\n\n‘Survobj’ is a variable created by an R command during the process of a Kaplan–Meier estimate, and indicates a survival object. ‘Inopioid_c’ is a newly created categorical variable based on ‘Inopioid’, which is coded as 0 for an opioid not used or 1 for an opioid used during operation. From left, each column contains each coded variable: The first column has a number automatically generated by R, the variable ‘No’ is a coded number in the original data, ‘Antiemetics’ has a value of 0 for Drug A and 1 for Drug B, ‘Age’ and ‘Wt’ are the actual patients’ age and body weight, ‘Inopioid’ is the amount of opioid used during surgery, ‘Time’ indicates the onset time of postoperative nausea and vomiting, and ‘PONV’ is coded as 1 when the patient experienced postoperative nausea and vomiting.\n\n##### Table 8.\nResults of Stratified Cox Proportional Hazard Model. Stratification with ‘Inopioid_c’\nCall: coxph(formula = Surv(Time, PONV == 1) ~ Antiemetics + strata(Inopioid_c), data = PONV.raw)\nn = 104, number of events = 63\ncoef exp(coef) se(coef) z Pr(>|z|)\nAntiemetics 0.7282 2.0714 0.2625 2.774 0.00553**\n---\nSignif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘’\n\nexp(coef) exp(-coef) Lower .95 Upper .95\n\nAntiemetics 2.071 0.4828 1.238 3.465\nConcordance = 0.634 (se = 0.034)\nRsquare = 0.074 (max possible = 0.979)\nLikelihood ratio test = 7.96 on 1 df, P = 0.005\nWald test = 7.7 on 1 df, P = 0.006\nScore (logrank) test = 8.03 on 1 df, P = 0.005\n\n‘Antiemetics’ is coded as 0 for Drug A or 1 for Drug B in the original data. ‘Inopioid_c’ is a newly created categorical variable based on ‘Inopioid’, which is coded as 0 for an opioid not used or 1 for an opioid used during operation. coef: the value of coefficient, exp(coef): exponential value of coefficient, se(coef): standard error of coefficient, z: z-statistics, Pr(>|z|): P value of given z-statistics, Signif. codes: codes for significance marking.\n\n##### Table 9.\nData Divided by survSplit Function\nNo Antiemetics Age Wt Inopioid Survobj Inopioid_c id tstart Time PONV tgroup\n1 1 0 48 78.5 0 4+ 0 1 0 3 0 1\n2 1 0 48 78.5 0 4+ 0 1 3 4 0 2\n3 3 0 54 88.3 100 21+ 1 2 0 3 0 1\n4 3 0 54 88.3 100 21+ 1 2 3 6 0 2\n5 3 0 54 88.3 100 21+ 1 2 6 21 0 3\n\nAll personal data are separated according to a preset time period (at 3 and 6 h). The same ‘id’ number indicates the same person. For example, data with id = 1 are separated into two time periods. The first period starts from time = 0 (tstart = 0) and ends at 3 (Time = 3) and PONV does not occur. The second period starts from 3 to 4 (the observation is prematurely ended before 6) and PONV does not occur. The same time period is indicated as tgroup (time group) in the last column. The other variables are the same as in Table 7.\n\n##### Table 10.\nResults of Time-dependent Coefficient Cox Regression Using Step Function and Schoenfeld Residual Test\nCall: coxph(formula = Surv(tstart, Time, PONV) ~ Antiemetics:strata(tgroup) + Inopioid, data = tdc)\nn = 250, number of events = 63\ncoef exp(coef) se(coef) z Pr(>|z|)\nInopioid 0.012477 1.012556 0.002413 5.172 2.32E-07***\nAntiemetics: strata(tgroup)tgroup = 1 1.295949 3.654464 0.567181 2.285 0.02232*\nAntiemetics: strata(tgroup)tgroup = 2 1.360185 3.896914 0.521567 2.608 0.00911**\nAntiemetics: strata(tgroup)tgroup = 3 −0.063743 0.938247 0.404993 −0.157 0.87494\n---\n\nSignif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\nexp(coef) exp(-coef) Lower .95 Upper .95\n\nInopioid 1.0126 0.9876 1.0078 1.017\nAntiemetics: strata(tgroup)tgroup = 1 3.6545 0.2736 1.2024 11.107\nAntiemetics: strata(tgroup)tgroup = 2 3.8969 0.2566 1.4020 10.831\nAntiemetics: strata(tgroup)tgroup = 3 0.9382 1.0658 0.4242 2.075\nConcordance  = 0.67 (se = 0.031)\nRsquare  = 0.152 (max possible = 0.874)\nLikelihood ratio test  = 41.35 on 4 df, P = 2e-08\nWald test  = 38.92 on 4 df, P = 7e-08\nScore (logrank) test  = 44.61 on 4 df, P = 5e-09\n\nResults of Schoenfeld residual test\nrho chisq P\n\nInopioid 0.29948 5.150327 0.0232\nAntiemetics: strata(tgroup)tgroup = 1 −0.02755 0.047411 0.8276\nAntiemetics: strata(tgroup)tgroup = 2 −0.00368 0.000845 0.9768\nAntiemetics: strata(tgroup)tgroup = 3 0.02486 0.038692 0.8441\nGLOBAL NA 5.199691 0.2674\n\n‘Antiemetics’ is coded as 0 for Drug A or 1 for Drug B in the original data. ‘Inopioid’ is the amount of opioid used during surgery. The split time periods are presented as Antiemetics:strata(tgroup)tgroup = 1 for the time period from 0 to 3, Antiemetics:strata(tgroup)tgroup = 2 for the time period from 3 to 6, and Antiemetics:strata(tgroup)tgroup = 3 for the time period from 6 to the end of the observation. coef: the value of coefficient, exp(coef): exponential value of coefficient, se(coef): standard error of coefficient, z: z-statistics, Pr(>|z|): P value of given z-statistics, Signif. codes: codes for significance marking.\n\n##### Table 11.\nComparison Kaplan–Meier Analysis and Survival Analysis with Time-dependent Coefficient\nKaplan–Meier analysis\nn Events Median 0.95LCL 0.95UCL\nAntiemetics = 0 51 25 13 10 NA\nAntiemetics = 1 53 38 6 5 12\n\nSurvival analysis with time-dependent coefficient\nn Events Median 0.95LCL 0.95UCL\n\n0 104 126 31 17 40\n1 104 126 16 10 26\n\nProportional hazard assumed Kaplan–Meier analysis results are presented in the upper part of the table. Note that this result is the same as in Table 3. The lower part of this table presents the results of a Cox regression with a time-dependent coefficient. The median survival is different from the proportional hazard assumed analysis. Antiemetics = 0 and 1 indicate Drugs A and B respectively. n: total number of cases, Events: number of patients who experienced postoperative nausea and vomiting, 0.95LCL: lower limit of 95% confidence interval, or 0.95UCL: upper limit of 95% confidence interval.\n\n### References\n\n4. Hancock MJ, Maher CG, Costa Lda C, Williams CM. A guide to survival analysis for manual therapy clinicians and researchers. Man Ther 2014; 19: 511-6.", null, "", null, "5. Kleinbaum D, Klein M. Evaluating the proportional hazards assumption. Survival Analysis. A Self-Learning Text. 2nd ed. New York, Springer Science+Business Media, Inc. 2005, pp 131-72.\n\n6. Schonfeld D. Partial residuals for the proportional hazards model. Biometrika 1982; 69: 238-41.", null, "", null, "7. Grambsch PM, Therneau TM. Proportional hazards tests and diagnostics based on weighted residuals. Biometrika 1994; 81: 515-26.", null, "", null, "8. Abeysekera W, Sooriyarachchi R. Use of Schoenfeld’s global test to test the proportional hazards assumption in the Cox proportional hazards model: an application to a clinical study. J Natl Sci Found 2009; 37: 41-51.\n\n9. Ekman A. Variable selection for the Cox proportional hazards model: A simulation study comparing the stepwise, lasso and bootstrap approach [Master's thesis]. [Umeå]: UMEÅUniversity;. 2017; 50 p. Available from http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-130521.\n\n10. Prashant Narayan KC. Extension of Cox PH Model When Hazards are Non-Proportional Applied to Residential Treatment for Drug Abuse [Master's thesis]. [Mankato (MN)]: Minnesota State University;. 2016; 51 p. Available from https://cornerstone.lib.mnsu.edu/etds/661/.\n\n11. Collett D. Testing the assumption of proportional hazards. Modelling Survival Data in Medical Research. 2nd ed. Boca Raton, Chapman & Hall/CRC. 2003, pp 141131-7.\n\n12. Kleinbaum D, Klein M. The stratified Cox procedure. Survival analysis. 2nd ed. New York, Springer Science+Business Media, Inc. 2005, pp 173-210.\n\n13. Collett D. Time-dependent variables. Modelling Survival Data in Medical Research. 2nd ed. Boca Raton, Chapman & Hall/CRC. 2003, pp 251-72.\n\n14. Zhang Z, Reinikainen J, Adeleke KA, Pieterse ME, Groothuis-Oudshoorn CG. Time-varying covariates and coefficients in Cox regression models. Ann Transl Med 2018; 6: 121.", null, "", null, "", null, "15. Thomas L, Reyes EM. Tutorial: survival estimation for Cox regression models with time-varying coefficients using SAS and R. J Stat Softw 2014; 61: 1-23.\n\n16. Wigmore TJ, Mohammed K, Jhanji S. Long-term survival for patients undergoing volatile versus IV anesthesia for cancer surgery: a retrospective analysis. Anesthesiology 2016; 124: 69-79.", null, "", null, "17. Tsui BC, Rashiq S, Schopflocher D, Murtha A, Broemling S, Pillay J, et al. Epidural anesthesia and cancer recurrence rates after radical prostatectomy. Can J Anaesth 2010; 57: 107-12.", null, "", null, "", null, "18. Biki B, Mascha E, Moriarty DC, Fitzpatrick JM, Sessler DI, Buggy DJ. Anesthetic technique for radical prostatectomy surgery affects cancer recurrence: a retrospective analysis. Anesthesiology 2008; 109: 180-7.", null, "", null, "19. Qiu P, Sheng J. A two‐stage procedure for comparing hazard rate functions. J R Stat Soc Series B Stat Methodol 2008; 70: 191-208.", null, "20. Li H, Han D, Hou Y, Chen H, Chen Z. Statistical inference methods for two crossing survival curves: a comparison of methods. PLoS One 2015; 10: e0116774.", null, "", null, "", null, "21. Abraira V, Muriel A, Emparanza JI, Pijoan JI, Royuela A, Plana MN, et al. Reporting quality of survival analyses in medical journals still needs improvement. A minimal requirements proposal. J Clin Epidemiol 2013; 66: 1340-6.", null, "", null, "Editorial Office\n101-3503, Lotte Castle President, 109 Mapo-daero, Mapo-gu, Seoul 04146, Korea\nTel: +82-2-792-5128    Fax: +82-2-792-4089    E-mail: [email protected]", null, "", null, "", null, "", null, "", null, "" ]

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[ "# Draw The Shear And Moment Diagrams For The Overhang Beam.", null, "", null, "Draw the shear and moment diagrams for the cantilever beam. 2 kN/m A 6 kN m 2m The free-body diagram of the beam's right segment sectioned through an.", null, "Answer to Draw the shear and Moment diagrams for the overhang beam. How the bending moment diagram of an overhanging beam will be if only we can draw the shear force diagram since it dictates the shape of bending moment . 6–5.", null, "Draw the shear and moment diagrams for the beam. 2 m.", null, "3 m. 10 kN.", null, "8 kN. 15 kNm.", null, "6–6. Draw the shear and moment diagrams for the overhang beam.", null, "A. 6–5. Draw the shear and moment diagrams for the beam.", null, "2 m. 3 m.", null, "10 kN. 8 kN.", null, "15 kNm. 6–6.", null, "Draw the shear and moment diagrams for the overhang beam. A.Shear and moment diagrams and formulas are excerpted from the Western Woods Use Book, 4th edition, and are provided herein as a courtesy of Western Wood Products Association. Introduction Notations Relative to “Shear and Moment Diagrams” E = modulus of elasticity, psi I = moment of inertia, in.4 L = span length of the bending member, ft.\n\nhome / study / engineering / civil engineering / civil engineering questions and answers / Draw The Shear And Moment Diagram For The Overhang Beam. Question: .", null, "Draw the shear and moment diagrams for the shaft. The bearings at A and D exert only vertical reaction on the schematron.org loading is applied to the pulleys at B and C and E.", null, "Draw The Shear And Moment Diagrams For Double Overhang Beam. October 17, Beam stress deflection mechanicalc solved draw the shear and moment diagrams for double 6 3 constructing influence lines using the muller breslau principle mechanics of materials chapter 4 shear and moment in .", null, "Shear and Moment Diagrams Procedure for analysis - the following is a procedure for constructing the shear and moment diagrams for a beam. The change in the shear force is equal to the area under the distributed loading.", null, "If the distributed loading is a curve of degree n, the shear will be a curve of degree n+1. Shear and Moment Diagrams.Free Beam Calculator | Bending Moment, Shear Force and Deflection Calculator | SkyCivSHEAR FORCE AND BENDING MOMENT DIAGRAM FOR OVERHANGING BEAM - Mechanical Engineering Professionals", null, "## 7 thoughts on “Draw the shear and moment diagrams for the overhang beam.”\n\n1.", null, "Bomb3750 says:\n\nVery useful piece\n\n2.", null, "Matter28 says:\n\nI think, what is it excellent idea.\n\n3.", null, "Scott B. says:\n\nIt was and with me. We can communicate on this theme. Here or in PM.\n\n4.", null, "Vlady W. says:\n\nIn my opinion you are mistaken. Let's discuss it.\n\n5.", null, "Anel L. says:\n\nIn my opinion you are not right. I am assured. Let's discuss it.\n\n6.", null, "Dave Q. says:\n\nIt is remarkable, rather useful piece\n\n7.", null, "Wiegandboy says:" ]

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[ "• :00Days\n• :00Hours\n• :00Mins\n• 00Seconds\nA new era for learning is coming soon", null, "Suggested languages for you:\n\nEurope\n\nAnswers without the blur. Sign up and see all textbooks for free!", null, "Q83E\n\nExpert-verified", null, "Found in: Page 102", null, "### Linear Algebra With Applications\n\nBook edition 5th\nAuthor(s) Otto Bretscher\nPages 442 pages\nISBN 9780321796974", null, "# Are elementary matrices invertible? If so, is the inverse of an elementary matrix elementary as well? Explain the significance of your answers in terms of elementary row operations.\n\nThe inverse of an elementary matrix is an elementary matrix of the same type.\n\nSee the step by step solution\n\n## Step 1: Definition of the invertible matrix\n\nAn invertible matrix is defined as a matrix A of the dimension ${n}{×}{n}$ and is called invertible if and only if there exists another matrix B of the same dimensions.\n\n## Step 2: Some constants that the matrix constructed are noninvertible\n\nWe prove that “The inverse of an elementary matrix is again an elementary matrix of the same type.\"\n\nAn elementary matrix of order n is obtained by performing exactly one elementary row operation on the identity matrix ${I}_{n}$.\n\n## Step 3: Type 1\n\nSuppose that an elementary matrix ${E}_{n×n}$ is obtained from ${I}_{n}$ by multiplying a row by a constant $k\\in \\mathrm{ℝ},k\\ne 0$ . Without loss of generality, suppose we multiply the second row of ${I}_{n}$ by k. Then we have\n\n$E=\\left[\\begin{array}{cccc}1& 0& -& 0\\\\ 0& k& -& 0\\\\ |& |& \\& 0\\\\ 0& 0& -& 1\\end{array}\\right]$\n\nThen we have\n\n${E}^{-1}=\\left[\\begin{array}{cccc}1& 0& -& 0\\\\ 0& 1/k& -& 0\\\\ |& |& \\& 0\\\\ 0& 0& -& 1\\end{array}\\right]$\n\nNotice that ${E}^{-1}E={I}_{n}=E{E}^{-1}$\n\nTherefore ${E}^{-1}$ is obtained from by multiplying a row by $\\frac{1}{k}\\left(\\frac{1}{k}{R}_{a}↔{R}_{a}\\right)$. Hence is invertible and ${E}^{-1}$ is also an elementary matrix.\n\n## Step 4: Type 2\n\nSuppose that an elementary matrix ${E}_{n×n}$ is obtained from ${I}_{n}$ by interchanging two rows $\\left({R}_{i}↔{R}_{j}\\right)$. Without loss of generality, suppose we interchange the first and second row of ${I}_{n}$ . We have\n\n$E=\\left[\\begin{array}{cccc}1& 0& -& 0\\\\ 0& 0& -& 0\\\\ |& |& \\& 0\\\\ 0& 0& -& 1\\end{array}\\right]$\n\nThen we have\n\n${E}^{-1}=\\left[\\begin{array}{cccc}0& 1& -& 0\\\\ 1& 0& -& 0\\\\ |& |& \\& 0\\\\ 0& 0& -& 1\\end{array}\\right]=E$\n\nNotice that ${E}^{-1}E={I}_{n}=E{E}^{-1}$\n\nTherefore ${E}^{-1}$ is obtained from ${I}_{n}$ by interchanging same rows of ${I}_{n}\\left({R}_{i}-{R}_{j}\\right)$ . Hence E is invertible and ${E}^{-1}$ is also an elementary matrix.\n\n## Step 5: Type 3\n\nSuppose that an elementary matrix ${E}_{n×n}$ is obtained from ${I}_{n}$ by adding a multiple of one row to another $\\left({R}_{i}+k{R}_{j}\\to {R}_{i}\\right){R}_{i}+k$ . Without loss of generality, suppose we add k times second row of ${I}_{n}$ in first row ${I}_{n}$. of Then we have\n\n$E=\\left[\\begin{array}{cccc}1& k& -& 0\\\\ 0& 1& -& 0\\\\ |& |& \\& 0\\\\ 0& 0& -& 1\\end{array}\\right]$\n\nand\n\n${E}^{-1}=\\left[\\begin{array}{cccc}1& -k& -& 0\\\\ 0& 1& -& 0\\\\ |& |& \\& 0\\\\ 0& 0& -& 1\\end{array}\\right]$\n\nNotice that ${E}^{-1}E={I}_{n}=E{E}^{-1}$\n\nTherefore ${E}^{-1}$ is obtained from ${I}_{n}$ by subtracting a multiple of one row to another $\\left({R}_{i}-k{R}_{j}\\to {R}_{i}\\right)$. Hence E is invertible and ${E}^{-1}$ is also an elementary matrix.\n\n## Step 6: The final answer\n\nThe inverse of an elementary matrix is an elementary matrix of the same type.", null, "### Want to see more solutions like these?", null, "" ]

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[ "9 steps for this example. where: R1 is the resistance of the 1st resistor, measured in Ohms (ω). Voltage divider! All that's needed is a couple resistors whose ratio will divide a 5V signal to about 3. Various models are produced depending on the application (air, oil, potted, etc. The name Voltage Divider Bias is given in the fact that the voltage is divided between the R1 and R2. The output voltage is given by:. Problem using Simple Voltage Divider Circuits. ) 3 Add load resistor R L in parallel to R 2. As you can see, the voltage drop across all of the resistors will add up to the power supply voltage. Enter any of the three. Only R4 is connected to ground. Specifically, build a circuit with four resistors in series, calculate and measure the voltages across each one. The actual input threshold voltage varies because of the leakage current, and can be calculated with Equation 4. Small aperture antennas for RKE applications can be terminated either as a shorted or open loop within a fob. High voltage resistor divider probes designed specifically for this purpose can be used to measure voltages up to 100 kV. Any variation in the output device's voltage will create a proportional variation in the adjusted voltage at the output of the divider circuit. It can be created using two resistors as shown in figure 2. Dropping down from 5v to 3v is a 2v drop, that gives us a resistor ratio of 2:3 (drop 2 volts down to 3v), or 0. 3V for the Pi. As a test, if you input resistances of 3, 9 and 18 ohms, your answer should be 2 ohms. The problem is, what do you do with that ~3. The four variables involved in a two-resistor voltage divider are input voltage, output voltage, resistance 1, and resistance 2. A voltage divider circuit is a very common circuit that takes a higher voltage and converts it to a lower one by using a pair of resistors. Then, the spreadsheet formula in cell D3 is =96*LOG(B3/C3-1), which returns a value of +16. I S R 1 R 2 R i 3 R2 Want to know i R2. *Updated January 8, 2011 to accept/change commas to periods for those that use commas as decimal separators. A voltage divider involves applying a voltage source across a series of two resistors. Then we need to experiment with higher voltage divider resistor values and see how the voltage will be affected by them and find the point where we can't have greater voltage variation depending on the input resistance. 0V from a 6. The ratio of the resistor #1 to resistor #2 would be 0. The voltage divider is the series of resistors or capacitors which that can be tapped at any intermediate point to generate a specific fraction of the voltage applied between its ends. 3: Current Divider Formula = × Using this formula you can work out the currents flowing through individual resistors. What a voltage divider circuit looks like. Also as with resistor dividers, the divider ratio of a capacitive voltage divider is not affected by changes in the signal frequency even though the capacitor reactance is frequency dependent. The supply Voltage is divided up between the two resistances to give an output Voltage Vo which is the Voltage across R2. This calculator is based on the Ohms Law Calculator, but takes into consideration the voltage drop from the LED. This can be built into a FLEXI-BOX and a transmission line PCB is available which easily adapts for this circuit with a simple trimming operation. And there are certainly a few showing very simple physical circuits using alligator clips and/or breadboards. The voltage divider can help level the voltage down from a microcontroller (eg. Resistor Value and Ratio Calculator. Problem using Simple Voltage Divider Circuits. Hence the voltage drops across each resistor are proportional to their ohmic value. A calculator details how to specify the Determine the Open-Load Threshold-Voltage Range The standard resistor values for R1 and R2 have now been the maximum voltage value for the center point of the resistor-divider is: Next we pick a standard resistor for R2 from the E96 … Fetch Here. Voltage divider rule for DC circuit; Voltage divider rule for AC circuit; Voltage divider calculator; Voltage divider rule for DC circuit. It is very similar to the one in the link above, but I am using 3 10k resistors instead of 1 10k and 1 20k. 3) Do the calculation again but this time for the second voltage divider. Real-life voltage divider applications. I used an online tool to check the values before purchasing any parts. The voltage divider has two resistors in series. This calculator determines the resistance of up to 10 resistors in parallel. The two resistor voltage divider is used often to supply a voltage different from that of an available battery or power supply. Multiplier suffixes such as M for meg, u for micro etc. The trick here is not the specific value of any resistor, but the relationship between two resistors. The 1121 provides an interface to non-Phidgets resistance sensors such as: Force-Sensing Resistors (FSR), light sensors, thermistors (heat sensors), and bend sensors. This is a voltage divider, a simple circuit that can be used to derive a reference voltage from a known supply voltage. LDR’s (Light dependent resistors) have a low resistance in bright light and a high resistance in the darkness. 125 (if you have 1/8 watt resistors). This online tool is very easy to use and understand. Try making an amplifer were the voltage across the collector resistor is 3 volts, the voltage across the emitter resistor is 3 volts and the collector-emitter voltage of the transistor is 6 volts with the battery 12 volts. 0 volts across Rb while drawing no more than 10mA from the power supply. To calculate the Output Voltage enter Input Voltage, Resistor R1 and. It has four text fields which require you to enter the total voltage, the resistance of the first, second and third load. Sometimes you want to use a potentiometer to produce a voltage reference between two points on a range, for example if your supply voltage is 12v, you might want to use a potentiometer to give a reference between 3 and 10v. A current divider circuit contains various impedances in parallel. For a junction field-effect transistor (JFET) under certain operating conditions, the resistance of the. Potentiometer Equation and Calculator. In the op amp comparator circuit below, the potential driver network of two 10 K resistors give a fixed voltage on Pin 3 equal to half the supply voltage. 2V which may be a bit easier on the ESP8266. I strongly recommend you to replace one resistor with trimmer resistor to calibrate it to right value. Current limiting Resistor calculator for leds. Hi, i want to measure AC voltages of 3-phase supply using micro-controller through ADC. 125 (if you have 1/8 watt resistors). Specifically, build a circuit with four resistors in series, calculate and measure the voltages across each one. This is the name we give to a simple circuit of two series resistors. At that point, we (in general) have good choice of voltage divider resistors. Voltage divider calculator: calculates the voltage drops on each resistor load, when connected in series. Manufacturer of High Voltage Resistors, High Voltage Dividers, Precision Resistors and other resistive products such as Power Resistors, SMD High Voltage Resistors and Resistor Networks. Potentiometer Equation and Calculator. 01X range, 3 more resistors are used in exactly the same way as previously. See the complete profile on LinkedIn and discover Katrina’s. Figure 32: Resistance to Voltage. You can go from 9VDC to 3. equivalent of the simple network (using parallel resistors for R Th and a potential divider for V Th). EE301 - PARALLEL CIRCUITS AND KIRCHHOFF’S CURRENT LAW 3 Example: Determine the unknown currents in the circuit shown below. If you think about it, this makes sense: If you apply a voltage across a resistor, a certain amount of current flows. 3V for the Pi. The Voltage Divider Calculator an online tool which shows Voltage Divider for the given input. Two 100kohm resistors divide the voltage from 7. Voltage Divider Circuit. The four variables involved in a two-resistor voltage divider are input voltage, output voltage, resistance 1, and resistance 2. The purpose of the voltage divider in my last application was to provide the 3-5V to the Vcc pin of my DS1802 digital pot. Solving for power dissipated supplied in simple circuit youtube. Calculators: • Resistor color codes - calculate the resistance of resistors by selecting the colors of the bands • SMD resistor codes - calculate the resistance of SMD resistors by entering the number • LED resistor calculator - calculate the needed. This is handy because resistors are really cheap and usually they are sold in packs of 5, 10 or more. It’s extremely useful to know! If you know how the voltage divider works you can easily make sensor circuits or calculate values in a more complex circuit. Use an online resistance calculator to find the resistor values for the voltage divider circuit. Note: All results are rounded to 3 decimal places. Voltage divider. It's output voltage is a fixed fraction of its input voltage. We say that the circuit is \"loaded\". 7Ω so the voltage drop caused by this load will be 0. As shown in figure 1, if we have two resistors in series with values Ra and Rb, the equivalent resistance is the sum of both. The voltage that appears across the sensor (or the reference resistor) is then buffered before being sent to the ADC. If a resistor drops 50% of the total battery voltage in a voltage divider circuit, that proportion of 50% will remain the same as long as the resistor values are not altered. You need to find a divider that will change 5 into 3. Welcome to the Voltage Drop Formula website. Module 3: Amplifiers. Voltage divider design Detector electronics. The output at \"Vout\" represents the voltage across the resistor R2. A calculator details how to specify the Determine the Open-Load Threshold-Voltage Range The standard resistor values for R1 and R2 have now been the maximum voltage value for the center point of the resistor-divider is: Next we pick a standard resistor for R2 from the E96 … Fetch Here. Generally, Vout is used as a reference voltage. But like resistors, the capacitive voltage divider circuit is not affected by the changes in the frequency even though it uses reactive elements. Current Draw - How much does this device circuit to draw the voltage in AMPS; Required Dropping Resistor - The Series Resistor in ohms (Ω) Minimum Resistor Wattage - The Minimum resistor wattage, this is actually what the circuit draws so you should use a larger value to keep the resistor from over heating. (a) Determine the equivalent resistance (Req), (b) use Ohm’s Law to determine the circuit current, (c) use Ohm’s Law to determine the current through each resistor. Voltage divider rule for DC circuit. Whatever your application, IET Labs has a voltage divider solution. Capacitors in series. A voltage divider (also known as a potential divider) consists of two resistances R a and R b connected in series across a supply voltage V in. This calculator can determine the resistance of up to 10 resistors in parallel. Enter all resistors in Ohm or all in KOhm. Sponsored By. 350/291u = 1. 3V) to avoid damage to the sensor which makes it safe for the sensor to handle. Sometimes it is useful to be able to divide the potential of a circuit so that an output voltage that is a known fraction of the input voltage (known as a reference voltage) can be obtained. If an input voltage of 9 volts is applied to the circuit, calculate the value of the voltage drop across each of the resistors, using the voltage divider formula. V R1 ∝ R 1 and V R2 ∝ R 2 etc. A general guide to DC link capacitor design for Tesla coils and large power inverters. The resistor closest to input voltage is R1 and the one closest to ground is R2. Resistor Voltage Divider Calculator: This calculator will try to calculate the best resistors to use for a set of given input and output voltages. The ratio of the two resistors used determines the amount that the voltage is reduced. Most variable resistors are adjusted by mechanical movement (linear or rotary). The voltage divider is the series of resistors or capacitors which that can be tapped at any intermediate point to generate a specific fraction of the voltage applied between its ends. 3 Easy Steps to Make a Voltage Divider: For another project of mine, I needed a voltage divider from 12V to 5V. ElectroDroid is a simple and powerful collection of electronics tools and references. 1 Entering three or four values calculate the others. T Attenuator Calculator Calculates the resistor values, attenuation, 'impedance', reflection coefficient, VSWR and return loss of a T attenuator. / Voltage Divider Circuits Voltage Divider Circuits AC Electric Circuits Question 1 Don’t just sit there! Build something!! Learning to mathematically analyze circuits requires much study and practice. If you want bonus points (challenge yourself!), derive an algorithm to calculate a general voltage divider chain made from arbitrary resistors Rs1, Rp1, Rs2, Rp2! $\\endgroup$ – CuriousOne Oct 13 '14 at 8:39. Take a simple voltage divider composed of R1 and R2: Vout = V(R2/(R1 + R2)) How much would the output vary with temperature if each resistor was spec'd at +/- 100ppm/degree? In other words, how well would the resistors track if both were of the same type such as metal film, 1/10 watt chip resistors?. Voltage divider rule. Calculate the \"bleeder current. The voltage drop across the resistor R2 forward bias the Base-Emitter Junction, and the voltage divider bias circuit is designed so that the base current is much smaller than the I2 through R2. The output at \"V out\" represents the voltage across the resistor R2. Your battery will not last long with these resistors attached. the formula for calculating the output voltage is based on ohms law and is shown below. It comprises resistors 1 and 2, but between them the voltage is output somewhere else. Let’s look at the diagram that we have in front of our eyes. Resistor-Capacitor (RC) Time Constant Calculator. The two resistor voltage divider is one of the most common and useful circuits used by engineers. A voltage divider consists of two 56 kΩ resistors and a 15 V source. 4 is a schematic of a stacked emitter follower using the divider according to the principles of the present invention;. We will take it to controlled IC2 and IC3 again, by through diode D1 and VR1 to pin 5 of both IC. We will put. How Electronic Circuits Work Free Download - 100% Download Link Confirm. For the non-inverting resistors, I could have used the same resistors 10k and 80k if the reference voltage was 1. Voltage divider rule. calculators, engineering calculators Enter value and click on calculate. This fraction of the input voltage is proportional to the ratio of the two resistors. 5mA! P-FET User comments on the Jee Labs blog points to using a voltage divider with the top leg switched by P-FET using a capacitor pulsed gate. Foil resistors have had the best precision and stability ever since they were introduced in 1958. These calculators perform calculations for potential divider circuits. Voltage Divider Calculator The Voltage Divider refers to a device consisting of a resistor or series of resistors connected across a source of voltage and having one or more fixed or adjustable intermediate contacts where from any two terminals a desired reduced voltage may be obtained. Voltage Divider: this shows a voltage divider, which generates a reference voltage of 7. 5 %) LEADED FILM RESISTORS VISHAY INTERTECHNOLOGY, INC. Anyway you can drop the voltage by using the last concept explained above, or you can also use an LM338 IC variable voltage regulator to adjust the output to 3V. (wikipedia). High voltage resistor divider probes designed specifically for this purpose can be used to measure voltages up to 100 kV. The formula for calculating the output voltage is based on Ohms Law and is shown below. Voltage Divider Formula Vout = [R2 / {R1 + R2 ] * Vin. A voltage divider consists of two resistances R1 and R2 connected in series across a supply Voltage Vs. Clicking Calculate R1 and R2 will find the optimum pair of resistors from the selected range of preferred values, for a given V in and V out. Ok, here's the thing you can certain create a voltage divider $V_{IN}*\\frac{R2}{R1+R2}=V_{OUT}$, as Ilya Veygman completely discussed. Voltage Divider. Let's take an example of a potentiometer. Voltage Divider Calculator See our other Electronics Calculators. This product group comprises load and test resistors for laboratory environment, test field and industrial environment with different degrees of protection. voltage divider calculator; a voltage divider circuit is a very common circuit that takes a higher voltage and converts it to a lower one by using a pair of resistors. It also includes examples with a parallel circuit with three resistors and one with four resistors in parallel. Calculate/design series/parallel connection of resistors, capacitors and inductors: Charge time: Charge/discharge time for simple circuits (including 555). Assume the LiPo you are using outputs 4. Three resistors (labeled R1, R2, and R3), connected in a chain from one terminal of the battery to the other. You need to shift the Uno’s 5V signals to 3. So we are using 0. This may be a small enough loss to ignore in a practical circuit. it follows (potential divider) that A= 3:2 160 = 2V. Voltage divider circuit. JavaScript seems to be disabled in your browser. In some cases when we do not get the desires or specific resistor values we have to either use variable resistors such as potentiometers or presets to obtain such precise values. 3 ± 10% volts output. So one will be: V r1 = (680K / 900K) * 16 And the other: V r2 = (220K / 900K) * 16 Now that you have the voltage drop, you need to know the. Solution:. This calculator is based on the Ohms Law Calculator, but takes into consideration the voltage drop from the LED. Most resistors have four bands, but there are also resistors with three, five, and six bands. The source resistance R S is affected by R 3 (right). 3) Do the calculation again but this time for the second voltage divider. Welcome to EMH! EMH is the Electronics Math Helper. The easy method which should be followed here is to find the equivalent resistance first, and then to apply the original formula:. ) The Current Divider Our previous examination of resistors in series led to the concept of a voltage divider. Resistors in series When resistors are used in series, we can simplify the circuit to make calculations easier. If the 300uA doesn't vary much, then you won't waste very much current. For example, if you say input voltage 5, output 3. Calculator for voltage and current divider formula is also present. ‪Circuit Construction Kit: DC‬ - PhET Interactive Simulations. Practice by wiring three or four resistors together and then using a multimeter to measure the voltage across each of them. For example, suppose your circuit is powered by a 9 V battery, but your circuit really only needs 4. The output voltage is given by:. 3 is a schematic of a voltage divider according to the principles of the present invention including resistors setting the output resistance of the divider; FIG. Resistor Ratio Calculator Leslie Green / U. Across positive (+) and negative (-) of 22µF capacitor a very low voltage was measured and I was hoping for 8v. This is because in current dividers, total energy expended is. What a voltage divider circuit looks like. The formula for calculating the output voltage is based on Ohms Law and is shown below. For a DC circuit with constant voltage source V T and resistors in series, the voltage drop V i in resistor R i is given by the formula:. A potentiometer or a resistor a pot, is a three-terminal resistor with a sliding or rotating contact that forms an adjustable voltage divider. Voltage across R 2 = IR 2 = 1mA x 2kΩ = 2V. The required output voltage (V OUT) can be obtained across the resistor R2. This is handy because resistors are really cheap and usually they are sold in packs of 5, 10 or more. ) Power Supply Ripple and Noise Measurements ▸ Amplifier Design • Amplifiers. Anyway you can drop the voltage by using the last concept explained above, or you can also use an LM338 IC variable voltage regulator to adjust the output to 3V. The lower resistor has a xed resistance R. RESISTORS FOR HIGH VOLTAGE APPLICATIONS - Application Note Voltage Dividers A common application for high voltage resistors is in voltage dividers for the measurement or control of high voltage rails. Our voltage divider can be custom built to your specifications, so you do not have to pay for what you don't need. Figure 32: Resistance to Voltage. 3 Easy Steps to Make a Voltage Divider: For another project of mine, I needed a voltage divider from 12V to 5V. Day 2-3: Voltage divider design Select resistor values to obtain 2. 2K When the temperature is in the center of the window range, the voltage at pins 5 and 6 will be 1/2 the supply voltage, or 6 volts in this case. The supply voltage is divided between the two resistances to give an output voltage V out which is the voltage across R b. Online calculator for calculating resistive voltage divider automatically. Voltage Divider Again: Now return to the voltage divider configuration, but consider several resistors in series. In fact, most volume pots in guitars and amplifiers work as voltage dividers. At that point, we (in general) have good choice of voltage divider resistors. Calculate the \"bleeder current. Two 100kohm resistors divide the voltage from 7. The schematic representation of an op-amp is shown to the left. Voltage divider! All that's needed is a couple resistors whose ratio will divide a 5V signal to about 3. A voltage divider circuit is very simple circuit built by only two resistors (R1 and R2) as shown above in the circuit diagrams. The calculator also plots the circuit diagram and generates the component values. This is because in current dividers, total energy expended is. If the 300uA doesn't vary much, then you won't waste very much current. It consists of an electric circuit composed of two resistors and one input voltage supply. Calculator for biasing potentiometers between two voltages. Part 5 It becomes clear, then, that two equal resistors will divide the source voltage into two equal voltages (half of the source's voltage is dropped across each resistor). is it correct? 3) see attachment , resistors 1 must bigger ohm than resistor 2, correct? thanks JR63, you awesome man. Current Sense Resistors: Cost-Effective Current Flow Measurement. V L= R 2 R 1+R 2 V in. Guitar Amp Books for Professional Builders Books, Tutorials, and Technology for Guitar Amplifier Circuit Design. Example 1: Must calculate the resistors for a 5V to 1. The voltage to be added is determined by the values of two resistors R1 and R2 in a voltage divider. A simple example of a potential divider consists of two resistors in series, as shown in the diagram below. Say, you would like to track your battery's output voltage to not emptying it too much. A voltage divider (also known as a potential divider) consists of two resistances R a and R b connected in series across a supply voltage V in. The voltage divider is composed (usually) from a set of two resistors in series. Example 1: Must calculate the resistors for a 5V to 1. This Current Divider Calculator can calculate the current going through any branch in a parallel circuit, using the formula shown above. 125 (if you have 1/8 watt resistors). 06 mA times 10, or 0. Check corresponding boxes to get the total resistance for selected resistors. The potential across each resistor in series connection is dependent on the value of resistance. The voltage divider circuit consists of a voltage source and two resistors like 1k and 2k. An RC circuit is made by simply putting a resistor and a capacitor together as a voltage divider. The divide-down ratio is determined by two resistors. Difference amplifier calculator. 6KOhm to +5V instead, your voltage will be 3. Calculator for biasing potentiometers between two voltages. Keyword Research: People who searched voltage divider calculator also searched. Voltage Divider Calculator is wrong ? ohmslawcalculator dot com says i need so and so resistors to get desired voltage, but when i actually solder everything in place, results are close not not close enough. Voltage Divider Calculator. An electrical circuit has three parallel resistors of 100 ohms, 500 ohms, and 2000 ohms. Voltage Divider: this shows a voltage divider, which generates a reference voltage of 7. resistor divider free download. Figure 3-65. The supply voltage is divided between the two resistances to give an output voltage V out which is the voltage across R b. Typically, students practice by working through lots of sample problems and checking their answers against those. voltage divider is a chain of resistors linked end to end (in series). With R1 at 100kOhm and R2 at 68kOhm, the. The supply voltage is divided between the two resistances to give an output voltage V out which is the voltage across R b. Calculates resistors of the voltage divider network automatically. The required output voltage (V OUT) can be obtained across the resistor R2. Source: ohmslawcalculator. The two resistor voltage divider is one of the most common and useful circuits used by engineers. You could use a pair of resistors of equal value across the battery leads to provide the necessary 4. 2K When the temperature is in the center of the window range, the voltage at pins 5 and 6 will be 1/2 the supply voltage, or 6 volts in this case. Our voltage divider can be custom built to your specifications, so you do not have to pay for what you don't need. Figure 3-64 is used to illustrate the development of a simple voltage divider. If a device produces a voltage that varies over a range greater than 0 to 5 volts, a voltage divider can be used to reduce the voltage to within the range of 0 to 5 volts. Voltage divider. You need to find a divider that will change 5 into 3. Voltage Divider Calculator See our other Electronics Calculators. These resistor types are used for different applications like voltage divider, series resistor or as load resistor. The basic setup is made of two resistors: But choosing the right resistors is quite tricky. You can use this voltage divider calculator to determine any one of the four variables associated with a simple two-resistor voltage divider when the values of the other three variables are available. SMD resistors use numbers instead of colors. Image1: Simple voltage divider connected to ADC Image2: Calibrating ADC with voltage divider using voltmeter How to calibrate it. 3V) to avoid damage to the sensor which makes it safe for the sensor to handle. The trick here is not the specific value of any resistor, but the relationship between two resistors. here is a example of voltage divider calculator with 3 resistors. when measuring two or all phase-neutral supplies, i am getting mixed voltage values like 350V,440V respectively. The drawback of this is that most of the input current is wasted as heat in the resistors. To obtain a reasonably stable output voltage the output current should be a small fraction of the input current. The Voltage Divider Some particular circuits may need different B+ voltages, especially televisions, which commonly have sophiscated voltage divider circuits. Voltage Drop Calculator will perform calculations of electric values. You can simplify this to two resistors in series, the ten in parallel above are 39r/10 = 3. All resistors in series with each other share the same current but divide the input voltage. 1 volts to 1 volt. Note – There is also a color code for the voltage which is very useful in the capacitor component. Anyway you can drop the voltage by using the last concept explained above, or you can also use an LM338 IC variable voltage regulator to adjust the output to 3V. An RC circuit is made by simply putting a resistor and a capacitor together as a voltage divider. To calculate the voltage across any resistor in the potential divider, multiply the supply voltage (E) by the proportion of that resistor to the total resistance of all the resistors. 3V, so if you try to interface it with an Arduino (assume operating at 5V), something will need to be done to step down that 5V signal to 3. Below you can see the formula that you need to use to calculate the resistors that you need in your circuit: Solving the formula above with Vin=5V, R1=1000ohms and Vout=3. Calculator Three bands Four bands Five bands Six bands. A voltage / potential divider is a simple linear circuit that produces an output voltage (Vout) that is a fraction of its input voltage (Vin) mainly used in physics. Thevenin and Norton Equivalent Circuits: The Simplest Picture of a Black Box Source. 75 and R = 1. Just imagine a simple parallel circuit with 2 resistors, we can calculate the current simply using the formula, but what if there is 3 parallel resistors? can we use the same. Dividing 93. Voltage divider calculator lets you calculate the output potential dropped across the resistor. Welcome to EMH! EMH is the Electronics Math Helper. Input these values in our parallel resistor calculator. In fact, most volume pots in guitars and amplifiers work as voltage dividers. 3) Do the calculation again but this time for the second voltage divider. Figure 1: A voltage follower has a gain of one, so (theoretically) the output voltage is equal to the input voltage. here is a example of voltage divider calculator with 3 resistors. They create an output voltage that is a fraction of the input voltage. The ratio of the resistors divides and input voltage down to a lower voltage. please enter Input voltage VT resistance R1,resistance R2,resistance R3 and click on calculate button for obtaining voltage drop Input total voltage: […]. A more complicated task is to pick resistors to satisfy a ratio. Potentiometer Equation and Calculator. A voltage divider is a fundamental circuit in the field of electronics which can produce a portion of its input voltage as an output. The requirement for this voltage divider is to provide a voltage of 25 volts and a current of 910 milliamps to the load from a source voltage of 100 volts. 8 or roughly 8 ohms. I attached a picture of my circuit. The primary purpose of this circuit is to scale down the input voltage to a lower value based on the ratio of the two resistors. Foil resistors have had the best precision and stability ever since they were introduced in 1958. Voltage Dividers and Network Resistors. ElectroDroid is a simple and powerful collection of electronics tools and references. These calculators perform calculations for potential divider circuits. You could use a pair of resistors of equal value across the battery leads to provide the necessary 4. The two resistor voltage divider is one of the most common and useful circuits used by engineers. Best app of its kind!!!!! I have used this app on my work Samsung for a long time now and was always mad it was not available on my iPhone. 2V which may be a bit easier on the ESP8266. 2 on the right. The voltage divider calculator is a useful tool which is used to find the voltage divided by a series circuit. In this problem, the current is entering to the the resistor from the negative terminal. Figure 3: A voltage divider with a voltage follower (unity gain amp) that allows VOUT to remain steady. The voltage drops for the two capacitors is same in both the examples where the frequency is different. The output. Voltage Divider Calculator No. The formula describing a current divider is similar in form to that for the voltage divider. Voltage Divider Calculator - Inch Calculator. Ok, here's the thing you can certain create a voltage divider $V_{IN}*\\frac{R2}{R1+R2}=V_{OUT}$, as Ilya Veygman completely discussed. A voltage divider is a circuit that divides a voltage between two resistors. Keyword Research: People who searched voltage divider calculator also searched. Three simple rules. The output at \"Vout\" represents the voltage across the resistor R2. Voltage and Current divider arrangements are the common in electronic circuits. Resistors in Series and Parallel Combinations In our previous post about resistors , we studied about different types of resistors." ]

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[ "", null, "CSS/HTML", null, "dreamveaver", null, "导航标题", null, "软件开发php 链式写法是什么\n\n 后台-系统设置-扩展变量-手机广告位-内容正文底部\n\nphp链式写法是“\\$tree->setAge()->setID()->setName();”，其中在php类中this指针指向类/对象本身，它就像一个绳子把类/对象和类的属性、函数连接起来。", null, "this指针在不同的编程语言中的功能差不多，具体的小细节不一样。但是有一个基础就是指向对象/函数/类本身。基于这个基础就可以实现链式写法。", null, "php程序的demo：\n\n<?php\n/**\n* Created by PhpStorm.\n* User: dell\n* Date: 2017/3/31\n* Time: 21:42\n*/\n/*\n*注释的规范写法：@param [参数类型] 参数名 参数解释\n* @return 返回值 [类型] 返回值名 返回值说明\n*/\n\nclass Tree{\nprivate \\$id ;\nprivate \\$name;\nprivate \\$age;\n/*\n*\n* @param null\n* @return null\n*\n*/\npublic function _construct()\n{\n//构造函数\n}\n/*\n*\n* @param [array] \\$arr 参数1\n* @return null\n*\n*/\npublic function init( \\$arr = array() )\n{\n//初始化函数\n\\$arrs = array();\n//设置默认参数\n\\$arrs = [\n'id'=> 1,\n'name'=> 'user',\n'age' => 18\n];\nif( !(is_array(\\$arr)) )\n{\n//如果传进来的数据不是数组则默认是id\n\\$this->id = intval( \\$arr );\n}\n\\$arrs = array_merge( \\$arrs , \\$arr );//合并数组\n//给类的属性赋值\n\\$this->id = \\$arrs['id'];\n\\$this->name = \\$arrs['name'];\n\\$this->age = \\$arrs['age'];\n}\n/*\n*\n* @param [int] \\$data 参数1\n* @return \\$this\n*\n*/\npublic function setID( \\$data = 0 )\n{\n//判断是不是数字\n\\$this->id =is_numeric( \\$data )? \\$data : intval(\\$data) ;//判断是否是数字，是赋值，否则转为数字在赋值\nreturn \\$this;//返回this指针\n}\n/*\n*\n* @param [string] \\$data 参数1\n* @return \\$this\n*\n*/\npublic function setName( \\$data = 'user' )\n{\n//判断是不是数字\n\\$this->name =is_string( \\$data )? \\$data : strval(\\$data) ;//判断是否是字符串，是赋值，否则转为字符串在赋值\nreturn \\$this;//返回this指针\n}\n/*\n*\n* @param [int] data 参数1\n* @return \\$this\n*\n*/\npublic function setAge( \\$data = 18 )\n{\n//判断是不是数字\n\\$this->age =is_numeric( \\$data )? \\$data : intval(\\$data) ;//判断是否是数字，是赋值，否则转为数字在赋值\nreturn \\$this;//返回this指针\n}\n};\n\n\\$tree = new Tree();\n\\$array = array();\n\\$array['id'] = 10;\n\\$array['age'] = 20;\n\\$tree->init(\\$array);\nvar_dump(\\$tree);//打印结果\n\\$tree->setAge()->setID()->setName();//链式写法\nvar_dump(\\$tree);//在打印看链式写法是否有效\n?>", null, "后台-系统设置-扩展变量-手机广告位-内容正文底部\n版权声明\n\n 留言与评论（共有 0 条评论）\n\n 验证码：", null, "后台-系统设置-扩展变量-手机广告位-评论底部广告位\n\n标签列表\n\nhttps://www.jcdi.cn/" ]

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[ "author Bernard Blackham Fri, 25 Jun 2004 17:51:24 +0000 (17:51 +0000) committer Bernard Blackham Fri, 25 Jun 2004 17:51:24 +0000 (17:51 +0000)\n\nindex c3f04bc..25a24b6 100755 (executable)\n@@ -1,10 +1,13 @@\n#!/usr/bin/python\n\n-import sys, os, string, socket, time, re\n+import sys, os, string, time, re, pwd\nimport pg\nfrom LATClient import LATClient\nfrom VendingMachine import VendingMachine\n\n+GREETING = 'UCC SNACKS'\n+PIN_LENGTH = 4\n+\nclass DispenseDatabase:\ndef __init__(self, vending_machine):\nself.vending_machine = vending_machine\n@@ -35,6 +38,54 @@ class DispenseDatabase:\nself.process_requests()\nnotify = self.db.getnotify()\n\n+def get_pin(uid):\n+       try:\n+               info = pwd.getpwuid(uid)\n+       except KeyError:\n+               return None\n+       if info.pw_dir == None: return False\n+       pinfile = os.path.join(info.pw_dir, '.pin')\n+       try:\n+               s = os.stat(pinfile)\n+       except OSError:\n+               return False\n+       if s.st_mode & 077:\n+               return None\n+       try:\n+               f = file(pinfile)\n+       except IOError:\n+               return None\n+       f.close()\n+       if not re.search('^'+'[0-9]'*PIN_LENGTH+'\\$', pinstr):\n+               return None\n+       return int(pinstr)\n+\n+def has_good_pin(uid):\n+       return get_pin != None\n+\n+def verify_user_pin(uid, pin):\n+       if get_pin(uid) == pin:\n+               info = pwd.getpwuid(uid)\n+               return info.pw_name\n+       else:\n+               return None\n+\n+def door_open_mode(vending_machine):\n+       print \"Entering open door mode\"\n+       v.display(\"DOOR  OPEN\")\n+       while True:\n+               v.wait_for_events(1)\n+               while True:\n+                       e = v.next_event()\n+                       if e == None: break\n+                       (event, params) = e\n+                       if event == DOOR:\n+                               if params == 1: # door closed\n+                                       v.display(\"BYE BYE!\")\n+                                       time.sleep(1)\n+                                       return\n+\nif __name__ == '__main__':\n# Open vending machine via LAT\nlatclient = LATClient(service = 'VEND', password = 'dmscptd')\n@@ -49,6 +100,106 @@ if __name__ == '__main__':\n\ndb = DispenseDatabase(v)\ndb.process_requests()\n+       cur_user = ''\n+       cur_pin = ''\n+       cur_selection = ''\n+\n+       scrolling_message = [GREETING]\n+       scrolling_wraps = False\n+       need_repaint = True\n+       timeout = None\n+       last_tick = time.time()\n+\nwhile True:\n+               if timeout != None and timeout > 0 and time.time() > last_tick+1:\n+                       timeout -= 1\n+                       if len(scrolling_message) > 0:\n+                               need_repaint = True\n+               if need_repaint and len(scrolling_message) > 0:\n+                       v.display(scrolling_message)\n+                       if scrolling_wraps:\n+                               scrolling_message.append(scrolling_message)\n+                       del scrolling_message\n+                       need_repaint = False\n+\nv.wait_for_events(1)\n+               while True:\n+                       e = v.next_event()\n+                       if e == None: break\n+                       (event, params) = e\n+                       if event == DOOR:\n+                               if params == 0:\n+                                       door_open_mode(v);\n+                                       cur_user = ''\n+                                       cur_pin = ''\n+                                       scrolling_message = [GREETING]\n+                                       scrolling_wraps = False\n+                                       need_repaint = True\n+                       elif event == SWITCH:\n+                               # don't care right now.\n+                               pass\n+                       elif event == KEY:\n+                               key = params\n+                               # complicated key handling here:\n+                               if len(cur_user) < 5:\n+                                       if key == 11:\n+                                               cur_user = ''\n+                                               scrolling_message = [GREETING]\n+                                               scrolling_wraps = False\n+                                               need_repaint = True\n+                                               continue\n+                                       cur_user += chr(key + ord('0'))\n+                                       v.display('UID: '+cur_user)\n+                                       if len(cur_user) == 5:\n+                                               uid = int(cur_user)\n+                                               if not has_good_pin(uid):\n+                                                       v.display('PIN NO GOOD')\n+                                                       time.sleep(1)\n+                                                       continue\n+                                               v.display('PIN: ')\n+                                               continue\n+                               elif len(cur_pin) < PIN_LENGTH:\n+                                       if key == 11:\n+                                               if cur_pin == '':\n+                                                       cur_user = ''\n+                                                       scrolling_message = [GREETING]\n+                                                       scrolling_wraps = False\n+                                                       need_repaint = True\n+                                                       continue\n+                                               cur_pin = ''\n+                                               v.display('PIN: ')\n+                                               continue\n+                                       cur_pin += chr(key + ord('0'))\n+                                       v.display('PIN: '+'X'*len(cur_pin))\n+                                       if len(cur_pin) == PIN_LENGTH:\n+                                               name = verify_user_pin(int(cur_user), int(cur_pin))\n+                                               if name:\n+                                                       v.beep(0, False)\n+                                                       cur_selection = ''\n+\n+                                                       scrolling_message = [' WELCOME  ', name]\n+                                                       scrolling_message.append('OR A SNACK')\n+                                                       scrolling_wraps = True\n+                                                       need_repaint = True\n+                                               else:\n+                                                       v.beep(255, False)\n+                                                       scrolling_message = [' BAD PIN  ', '  SORRY   ', GREETING]\n+                                                       scrolling_wraps = False\n+                                                       need_repaint = True\n+\n+                                                       cur_user = ''\n+                                                       cur_pin = ''\n+                                                       continue\n+                               elif len(cur_selection) < 2:\n+                                       if key == 11:\n+                                               if cur_selection == '':\n+                                                       cur_pin = ''\n+                                                       cur_user = ''\n+                                                       v.display(GREETING)\n+                                                       continue\n+                                               cur_selection += chr(key + ord('0'))\n+                                               if len(cur_selection) == 2:\n+                                                       make_selection(cur_selection)\n+\n+\ndb.handle_events()", null, "UCC git Repository :: git.ucc.asn.au" ]

[ null, "http://ucc.asn.au/logos/ucc_sun_logo_black.png", null ]

[ "# Solved: histogram relative frequency\n\nThe main problem with histograms relative frequency is that they can be misleading. Histograms can be skewed in a number of ways, which can lead to inaccurate conclusions about the distribution of data.\n\n```\nimport matplotlib.pyplot as plt\n\n# frequencies\nages = [2,5,70,40,30,45,50,45,43,40,44,\n60,7]\n\n# setting the ranges and no. of intervals\nrange = (0, 10)\nbins = 5\n\n# plotting a histogram\nplt.hist(ages, bins=bins)\n\nplt.xlabel('age')\n\nplt.ylabel('No. of people')\n\nplt.title('Histogram of Age')```\n\n# function to show the plot\nplt.show()\nThis code is plotting a histogram of ages. The x-axis is age, the y-axis is the number of people, and the title is “Histogram of Age.”\n\nContents\n\n## Histograms\n\nHistograms are a way to visualize data in Python. They allow you to see how many occurrences of a particular value occur in a given dataset.\n\n## Frequency\n\nIn Python, frequency refers to the number of times a particular value occurs in a data set. For example, the frequency of the letter “A” in a text file is 1.\n\nRelated posts:" ]

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[ "# What is the second law of thermodynamics for dummies?\n\n## What is the second law of thermodynamics for dummies?\n\nSign up for early access to Dummies Drops In physics, the second law of thermodynamics says that heat flows naturally from an object at a higher temperature to an object at a lower temperature, and heat doesn’t flow in the opposite direction of its own accord. A heat engine turns heat into work.\n\nWhat is the best example of the second law of thermodynamics?\n\nExamples of the second law of thermodynamics For example, when a hot object is placed in contact with a cold object, heat flows from the hotter one to the colder one, never spontaneously from colder to hotter. If heat were to leave the colder object and pass to the hotter one, energy could still be conserved.\n\nHow do you solve the second law of thermodynamics?\n\nΔ S = Q T , Δ S = Q T , where Q is the heat that transfers energy during a process, and T is the absolute temperature at which the process takes place. Q is positive for energy transferred into the system by heat and negative for energy transferred out of the system by heat.\n\n### What is a real life example of the second law of thermodynamics?\n\nReal life Example of second law of thermodynamics is that: When we put an ice cube in a cup with water at room temperature. The water releases off heat and the ice cube melts. Hence, the entropy of water decreases.\n\nCan 2nd law of thermodynamics be violated?\n\nThe truth of the second law is a statistical, not a mathematical, truth, for it depends on the fact that the bodies we deal with consist of millions of molecules… Hence the second law of thermodynamics is continually being violated, and that to a considerable extent, in any sufficiently small group of molecules …\n\nWhy second law of thermodynamics is important?\n\nWhy is the second law of thermodynamics so important? Second law of thermodynamics is very important because it talks about entropy and as we have discussed, ‘entropy dictates whether or not a process or a reaction is going to be spontaneous’.\n\n## What are the limitations of second law of thermodynamics?\n\nThere are no limitations to the second law of thermodynamics. However, there is a misconception that the second law is only applicable to the closed system.\n\nWhy is the 2nd Law of thermodynamics important?\n\nSecond law of thermodynamics is very important because it talks about entropy and as we have discussed, ‘entropy dictates whether or not a process or a reaction is going to be spontaneous’.\n\nWhy is the second law of thermodynamics important?\n\n### What is the limitation of second law of thermodynamic?\n\nIs the second law of thermodynamics always true?\n\nThe laws of thermodynamics only hold true as statistical averages, and some think the second law won’t be so cast-iron on the very small scales of quantum physics where few particles are involved. The second law in its classical form also determines the ultimate fate of the universe.\n\nWho created second law of thermodynamics?\n\nNicolas Léonard Sadi Carnot was a French physicist, who is considered to be the “father of thermodynamics,” for he is responsible for the origins of the Second Law of Thermodynamics, as well as various other concepts.\n\n## What is the real second law of thermodynamics?\n\nThe Second Law of Thermodynamics states that when energy is transferred, there will be less energy available at the end of the transfer process than at the beginning. Due to entropy, which is the measure of disorder in a closed system, all of the available energy will not be useful to the organism. Entropy increases as energy is transferred.\n\nWhat are the first three laws of thermodynamics?\n\nThere three laws are: The first law of thermodynamics is the law of the conservation of energy; it states that energy cannot be created nor destroyed. An example is when the chlorophyll absorbs\n\nIs there any proof to 2nd Law of thermodynamics?\n\nWhile mathematical statements can have proof, fundamentally, physical laws can only be consistent with experimental evidence. It sounds weak, but in the case of the second law of thermodynamics there is a monumental amount of consistent experimental evidence.\n\n### What is the second rule of thermodynamics?\n\nThe second law of thermodynamics states that in a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems never decreases. Another form of the statement is that heat does not spontaneously pass from a colder body to a warmer body." ]

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[ "E. Tasty Dishes\ntime limit per test\n10 seconds\nmemory limit per test\n64 megabytes\ninput\nstandard input\noutput\nstandard output\n\nNote that the memory limit is unusual.\n\nThere are $n$ chefs numbered $1, 2, \\ldots, n$ that must prepare dishes for a king. Chef $i$ has skill $i$ and initially has a dish of tastiness $a_i$ where $|a_i| \\leq i$. Each chef has a list of other chefs that he is allowed to copy from. To stop chefs from learning bad habits, the king makes sure that chef $i$ can only copy from chefs of larger skill.\n\nThere are a sequence of days that pass during which the chefs can work on their dish. During each day, there are two stages during which a chef can change the tastiness of their dish.\n\n1. At the beginning of each day, each chef can choose to work (or not work) on their own dish, thereby multiplying the tastiness of their dish of their skill ($a_i := i \\cdot a_i$) (or doing nothing).\n2. After all chefs (who wanted) worked on their own dishes, each start observing the other chefs. In particular, for each chef $j$ on chef $i$'s list, chef $i$ can choose to copy (or not copy) $j$'s dish, thereby adding the tastiness of the $j$'s dish to $i$'s dish ($a_i := a_i + a_j$) (or doing nothing). It can be assumed that all copying occurs simultaneously. Namely, if chef $i$ chooses to copy from chef $j$ he will copy the tastiness of chef $j$'s dish at the end of stage $1$.\n\nAll chefs work to maximize the tastiness of their own dish in order to please the king.\n\nFinally, you are given $q$ queries. Each query is one of two types.\n\n1. $1$ $k$ $l$ $r$ — find the sum of tastiness $a_l, a_{l+1}, \\ldots, a_{r}$ after the $k$-th day. Because this value can be large, find it modulo $10^9 + 7$.\n2. $2$ $i$ $x$ — the king adds $x$ tastiness to the $i$-th chef's dish before the $1$-st day begins ($a_i := a_i + x$). Note that, because the king wants to see tastier dishes, he only adds positive tastiness ($x > 0$).\n\nNote that queries of type $1$ are independent of each all other queries. Specifically, each query of type $1$ is a scenario and does not change the initial tastiness $a_i$ of any dish for future queries. Note that queries of type $2$ are cumulative and only change the initial tastiness $a_i$ of a dish. See notes for an example of queries.\n\nInput\n\nThe first line contains a single integer $n$ ($1 \\le n \\le 300$) — the number of chefs.\n\nThe second line contains $n$ integers $a_1, a_2, \\ldots, a_n$ ($-i \\le a_i \\le i$).\n\nThe next $n$ lines each begin with a integer $c_i$ ($0 \\le c_i < n$), denoting the number of chefs the $i$-th chef can copy from. This number is followed by $c_i$ distinct integers $d$ ($i < d \\le n$), signifying that chef $i$ is allowed to copy from chef $d$ during stage $2$ of each day.\n\nThe next line contains a single integer $q$ ($1 \\le q \\le 2 \\cdot 10^5$) — the number of queries.\n\nEach of the next $q$ lines contains a query of one of two types:\n\n• $1$ $k$ $l$ $r$ ($1 \\le l \\le r \\le n$; $1 \\le k \\le 1000$);\n• $2$ $i$ $x$ ($1 \\le i \\le n$; $1 \\le x \\le 1000$).\n\nIt is guaranteed that there is at least one query of the first type.\n\nOutput\n\nFor each query of the first type, print a single integer — the answer to the query.\n\nExample\nInput\n5\n1 0 -2 -2 4\n4 2 3 4 5\n1 3\n1 4\n1 5\n0\n7\n1 1 1 5\n2 4 3\n1 1 1 5\n2 3 2\n1 2 2 4\n2 5 1\n1 981 4 5\n\nOutput\n57\n71\n316\n278497818\n\nNote\n\nBelow is the set of chefs that each chef is allowed to copy from:\n\n• $1$: $\\{2, 3, 4, 5\\}$\n• $2$: $\\{3\\}$\n• $3$: $\\{4\\}$\n• $4$: $\\{5\\}$\n• $5$: $\\emptyset$ (no other chefs)\n\nFollowing is a description of the sample.\n\nFor the first query of type $1$, the initial tastiness values are $[1, 0, -2, -2, 4]$.\n\nThe final result of the first day is shown below:\n\n1. $[1, 0, -2, -2, 20]$ (chef $5$ works on his dish).\n2. $[21, 0, -2, 18, 20]$ (chef $1$ and chef $4$ copy from chef $5$).\n\nSo, the answer for the $1$-st query is $21 + 0 - 2 + 18 + 20 = 57$.\n\nFor the $5$-th query ($3$-rd of type $1$). The initial tastiness values are now $[1, 0, 0, 1, 4]$.\n\nDay 1\n\n1. $[1, 0, 0, 4, 20]$ (chefs $4$ and $5$ work on their dishes).\n2. $[25,0, 4, 24, 20]$ (chef $1$ copies from chefs $4$ and $5$, chef $3$ copies from chef $4$, chef $4$ copies from chef $5$).\n\nDay 2\n\n1. $[25, 0, 12, 96, 100]$ (all chefs but chef $2$ work on their dish).\n2. $[233, 12, 108, 196, 100]$ (chef $1$ copies from chefs $3$, $4$ and $5$, chef $2$ from $3$, chef $3$ from $4$, chef $4$ from chef $5$).\n\nSo, the answer for the $5$-th query is $12+108+196=316$.\n\nIt can be shown that, in each step we described, all chefs moved optimally." ]

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[ "Categories", null, "Account", null, "# HP 300s+ HP300S+ Scientific Calculator\n\nProduct Code: HP HP 300s+ HP300S+ Scientific Calculator\nPrice: R250.00 R195.00\nEx Vat: R169.57\nQty:     - OR -", null, "0 reviews  |  Write a review\n\nHP 300s+ HP300S+ Scientific Calculator\n\n• Streamline prime factorization, whole number division, fraction reduction and GCF/LCM calculations with built in tools.\n• Perform decimal and hexadecimal conversions.\n• Convert from decimals to fractions.\n• Make metric and imperial unit conversions.\n• Easily enter one and two variable statistical data with table based editor.\n• Calculate mean, standard deviation, variance, regression analysis and more\n\n## Write a review", null, "" ]

[ null, "https://shp.lantis.co.za/image/data/Logos/pcbway_logo.png", null, "https://www.lantis.co.za/image/data/Youtube/yt_logo_rgb_light.png", null, "https://shp.lantis.co.za/catalog/view/theme/default/image/stars-0.png", null, "https://shp.lantis.co.za/index.php", null ]

[ "# Optimized Configurations of Kinematically Redundant Planar Parallel Manipulator following a Desired TrajectoryAcademic research paper on \"Materials engineering\"", null, "CC BY-NC-ND", null, "0", null, "0\nShare paper\nProcedia Technology\nOECD Field of science\nKeywords\n{\"Kinematic redundancy\" / \"planar parallel manipulator\" / \"staic force analysis\" / \"minimum joint torques\" / \"non-conventional optimization\"}\n\n## Abstract of research paper on Materials engineering, author of scientific article — K.V. Varalakshmi, J. Srinivas\n\nAbstract This paper presents an optimization methodology for achieving minimum actuation torques of a kinematically redundant planar parallel mechanism following a desired trajectory using binary coded Genetic Algorithms (GA). A user interactive computer program developed in present work helps for obtaining inverse kinematic solution and Jacobian matrices at a given Cartesian coordinate location of the end-effector. Furthermore, the joint torques are obtained from the end-effector forces (wrench) using Jacobian matrix at every location. The resultant joint torque vector can be used to describe the objective function. The variables of the optimization problem are redundant base prismatic joint displacements and the constraints include the variable bounds and the pre-defined trajectory lying within the original workspace. The outputs of the kinematically-redundant 3-PRRR manipulator are compared against the results for a non-redundant 3-RRR manipulator. The results show that the redundant manipulator gives relatively lower input torques. Also, it is observed that while passing through singular configurations on the trajectory, finite values of torques are achieved. Results are shown for a straight-line trajectory.\n\n## Academic research paper on topic \"Optimized Configurations of Kinematically Redundant Planar Parallel Manipulator following a Desired Trajectory\"\n\nAvailable online at www.sciencedirect.com\n\nScienceDirect\n\nProcedia Technology 14 (2014) 133 - 140\n\n2nd International Conference on Innovations in Automation and Mechatronics Engineering,\n\nICIAME 2014\n\nOptimized Configurations of Kinematically Redundant Planar Parallel Manipulator following a Desired Trajectory\n\nK V Varalakshmia * , J Srinivasa\n\na bDepartment of Mechannical Engg., National Institute of Technology, Rourkela, Odisha 769008, India\n\nAbstract\n\nThis paper presents an optimization methodology for achieving minimum actuation torques of a kinematically redundant planar parallel mechanism following a desired trajectory using binary coded Genetic Algorithms (GA). A user interactive computer program developed in present work helps for obtaining inverse kinematic solution and Jacobian matrices at a given Cartesian coordinate location of the end-effector. Furthermore, the joint torques are obtained from the end-effector forces (wrench) using Jacobian matrix at every location. The resultant joint torque vector can be used to describe the objective function. The variables of the optimization problem are redundant base prismatic joint displacements and the constraints include the variable bounds and the pre-defined trajectory lying within the original workspace. The outputs of the kinematically-redundant 3-PRRR manipulator are compared against the results for a non-redundant 3-RRR manipulator. The results show that the redundant manipulator gives relatively lower input torques. Also, it is observed that while passing through singular configurations on the trajectory, finite values of torques are achieved. Results are shown for a straight-line trajectory. © 2014 Elsevier Ltd.Thisis anopenaccess article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/3.0/).\n\nPeer-review under responsibility of the Organizing Committee of ICIAME 2014.\n\nKeywords: Kinematic redundancy; planar parallel manipulator; staic force analysis; minimum joint torques; non-conventional optimization\n\nNomenclature\n\nq joint displacements Hi unit vector directed along the distal links Pi prismatic joint limits\n\nx end-effector pose hi, l2i link lengths of active and passive links R rotation matrix\n\nJx inverse Jacobian e, active joint angles (z-1,2,3) Z unit vector along Z direction\n\nJq direct Jacobian ßi passive joint angles (z-1,2,3) F force vector\n\n* Corresponding author. Tel.: +918763989679; E-mail address: [email protected]\n\n2212-0173 © 2014 Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).\n\nPeer-review under responsibility of the Organizing Committee of ICIAME 2014. doi:10.1016/j.protcy.2014.08.018\n\nOP vector expressing point P a, prismatic joint angles (/=1,2,3) f objective function_PC, vector from P to C,- w.r.to xy\n\nt torque\n\n1. Introduction\n\nRedundancy in parallel manipulators is generally divided into kinematic redundancy and actuation redundancy here they explained in terms of mobility. When the manipulator mobility is larger than the required degrees of freedom (DOF), it is kinematic redundancy. On the other hand, when the number of actuators in the manipulator is larger than the mobility, it is actuation redundancy. However, most of the studies - have discussed on actuation redundancy, in this the manipulator is controlled with more actuators than the required without increasing the mobility. Recently some of the researches have been discussed on kinematic redundancy -. This type of redundancy can enhance the dexterity of the manipulator as well as enlarge the workspace. Additionally kinematically redundant parallel manipulators have been widely used to improve the trajectory tracking performance by effectively increasing the singularity-free region in the workspace. Wang and Gosselin and Ebrahimi et al. - studied the singularity of three new types of kinematically redundant parallel manipulators. It was shown that the singularity free configurations are significantly improved when compared to the non-redundant manipulator. Cha et al. - proposed a kinematic redundancy resolution algorithm for singularity avoidance of the 3-RRR mechanism and to determine the allowable ranges of the kinematically redundant active prismatic joint variables for a given trajectory to be in singularity free region. Most of the research works focused on dealing the kinematic design, workspace and singularity avoidance, very few authors dealt force capabilities of kinematically-redundant planar parallel manipulators. Weihmann et al. proposed an optimization-based method for determining the force capabilities of the 3-RPRR manipulator. Here path of the manipulator is not considered. Boudreau developed an optimization-based methodology for resolving the generalized forces for kinematically-redundant planar parallel manipulator following a desired trajectory and achieved improved results compared to non-redundant manipulator.\n\nPresent work concerns with the kinematic analysis of 3-PRRR kinematically redundant mechanism of three different degrees of freedom and gives attention on the determination of joint-torques using static force analysis. A suitable end-effector trajectory is selected and the nonlinear joint torques at each trajectory point are minimized by selecting optimum locations of prismatic joints on the base links using binary coded genetic algorithms. If it is of first order redundancy, random search may resolve the problem. Optimized torques are illustrated for a trajectory passing through singular points.\n\n2. Description of kinematically redundant linkages\n\nFig. 1 Redundant 3-PRRR manipulator configuration\n\nThe redundant 3-PRRR planar parallel manipulator as shown in Fig. 1 consists of a three branches, each composed of an actuated revolute joint fixed to the base, followed by passive revolute joints, one of which is attached to the moving platform (end-effector). If the points A, coincides with O, (, = 1, 2, 3), then the configuration is non-redundant 3-RRR manipulator. The basic configuration of redundant 3-PRRR mechanism is derived by adding extra active prismatic joints to the limbs of the 3-RRR manipulator. The added prismatic actuators allow any arbitrary base joints. Adding one degree of kinematic redundancy (1-DOKR) can considerably reduce the number of direct kinematic singularities of a 3-RRR planar manipulator up to certain extent . Hence, one degree of kinematic redundancy is added here in each case to each branch of the 3-RRR manipulator producing manipulators with 1-DOKR, 2-DOKR and 3-DOKR respectively. The added kinematic redundancies enable the manipulators to avoid kinematic singularities, improve their manoeuvrability, and enlarge their reachable and dexterous workspaces and also causes less dynamic effects due to the weight of the actuators when they are close to the base.\n\n3. Jacobian formulation for 3-RRR and 3-PRRR manipulators\n\nThe velocity equation showing the Jacobian matrices of the manipulators resulting from differentiating the nonlinear loop-closure equations f(q,x) = 0 of the input q = [0\\,62,63] (joint displacements) and output x = [x, y, (f]T (end-effector pose) variables, with respect to time, i.e.\n\nJ XK = J CI\n\nWhere Jx = öf(q, x)/dx and Jq =3f(q, x)/3q are (m x m) and (m x n) matrices respectively. Where m is the DOFs in the Cartesian space and n is the DOFs of the linkage (for non-redundant manipulator m - n; While, X and q are the end-effector and joint velocities, respectively. The overall Jacobian matrix J can be expressed as:\n\nJ \" JX Jq\n\nWhere Jx and Jq are direct and inverse Jacobian matrices respectively. Based on the inverse displacement , considering the geometry of the non-redundant 3-RRR planar parallel manipulator in Fig. 1, the loop closure equations can be written as by defining the unit vector n, directed along the distal links. The following relation can thus be obtained for each kinematic chain:\n\nl2, n, = OP + [R]PC,- AB,\n\nBy squaring on both sides of Eq.( 3) and applying the law of cosines\n\nl22,- = (OP + [R]PC - AB, )T (OP + [R]PC - AB,)\n\nWhere [R] =\n\ncos^ - sin^ sin^ cos^\n\nvector from P to C t expressed in the moving frame xy\n\nis the rotation matrix, OP is the vector expressing point P and PCi' is the\n\nDifferentiating Eq. (4) with respect to time, the following Jacobian matrix can be obtained:\n\n12in i\n\n+ Z T (PC i X 12iHi )<j> + 12in i\n\nlusin 0 i - l1icos 0 i\n\n0, = 0\n\nWhere Z is the unit vector along z direction\n\nIt can be expressed in matrix form for all three legs as:\n\n121H1T Z T( PC1 X121n1) \" x 0 0 \" e,\n\nl22 n2 Z T(PC2 x l22n2) y + 0 ^ 2 0 02 = 0\n\n123 n3 ZT(PC3 X l23n3)_ Ä 0 0 X 3 _ 03\n\nWhere Xi = lh l2i nT (sindi - cosdf)\n\nThe above Eq. (6) is similar to Eq. (1) represents the Jacobian matrices of non-redundant 3-RRR planar parallel manipulator.\n\nThe loop closure equations of 3-PRRR can be expressed from Fig.1 as:\n\n/2I n = OP + [R]PCt- OB i\n\n¡1 = (OP + [R]PCi - OBi )T (OP + [R]PCi - OBi)\n\nDifferentiating Eq. (8) with respect to time, the following Jacobian matrices can be obtained:\n\n+ Z T (PC i x l2i ni )(j> + l2i n T\n\nlliSin 0 i - l cos 0 i\n\n0< - l2i n T p i\n\ncos a i sin a i\n\nIt can be expressed in matrix form for all three legs of kinematically redundant linkages as: 1-DOKR:\n\nl21nT Z T( PC1 X l21n1)\" x 0 0\n\nl nT 22 2 ZT(PC2 X l22„2) y + 0 0 * 2 0\n\nl nT 23 3 Z T(PC3 X l23n3) A 0 0 0 ^3\n\nPi ¿1 ¿2 ¿3\n\n2-DOKR:\n\n121nT ZT(PC 1 X121 nx) ' x 0 0 0 \" ¿1\n\nI 22 n 2T Z T( PC 2 X l22 n 2 ) y + 0 0 5 2 X 2 0 P 2 = 0\n\n123 nT Z T( PC 3 X 123 n3) _ j _ 0 0 0 0 * 3 _ _ ¿3 _\n\n3-DOKR:\n\n' 22 2\n\n123 n T\n\nZ T( PC 1 X 121 n1) ZT(PC2 x l22n2)\n\nZT(PC3 x 123n3)\n\nx 1 11 0 0 0 0\n\n+ 0 0 4 2 1 2 0 0\n\nU _ 0 0 0 0 4 3 13\n\nWhere = -I n. (cosa. + sina.) (i=1, 2, 3). 2i i i iJ\n\nThe Eqs. (10, 11 and 12) are similar to Eq. (1) represents the Jacobian matrices of redundant 3-PRRR planar parallel manipulator. And the Jacobian matrices are dimensionally homogenized . The developed equations allow in the computation of the velocities of the revolute and prismatic actuators for both the non-redundant and redundant cases when the velocity of the moving platform is known. Under static conditions the relationship between the joint forces/torques and the end-effector wrench is :\n\nF = J 1 r (13)\n\nFor a specified end-effector wrench F in Eq. (13) the generalized actuation joint torques/forces are given by:\n\nr = J1 F (14)\n\n4. Optimization Procedure\n\nAn optimization scheme can be described as the determination of the optimum kinematic positions of base prismatic joints in order to minimize the actuator torques subjected to the variable constrains. The multiplicity of solutions allows for minimization of the actuated joint torques required to sustain a wrench on the end-effector while following a trajectory.\n\nThe optimization problem is written as:\n\nMinimize TT (15)\n\nSubject to: p <P<P (i=1,2, 3) (16)\n\n' i,min ' ' i,max\n\nThe optimization procedure is as follows, at each step of the trajectory: Step 1: for a given pose, define the geometric parameters manipulator Step 2: define a trajectory Step 3: start with initial point of the trajectory\n\nStep 4: generate random locations of the redundant prismatic joints within the bounds\n\nStep 5: compute new co-ordinates of the fixed platform vertices\n\nStep 6: using inverse kinematics numerically compute Jacobian at a point\n\nStep 7: apply wrench on the end-effector and compute required torques using Eq. (14)\n\nStep 8: minimize function f(p1,p2,p3) = rTr , using a Genetic Algorithms optimization routine\n\nStep 9: repeat the process from step 4 to step 8 until the trajectory has been completed.\n\nWhere p . and p denote the lower and upper joint limits that guarantee the link- interference-free trajectories\n\n' i,min ' i,max i i j ^\n\nfor the manipulator. As the joint torques are highly nonlinear functions of the joint variables, in present case, binary coded Genetic algorithms technique is employed for obtaining the configurations corresponding to minimum torque condition. Genetic algorithms being a stochastic global optimization tool can effectively solve such nonlinear formulation using three operators: reproduction, crossover and mutation. An initial population of feasible strings is updated for the next generation without losing good strings of the current population. Binary coded strings are employed for convenience and the minimum error tolerance is used as a termination criterion. More details of genetic algorithms can be found elsewhere .\n\n5. Results and Discussion\n\nThe manipulator is considered to be used for pick and place; machining or welding operations following a given trajectory. Here a straight-line trajectory was used to show the effectiveness of the optimization. It passes through the singular (force unconstrained) configurations of the non-redundant manipulator and the results were obtained for both the non-redundant and redundant manipulators. The straight-line path trajectory with platform moving from the center of the workspace right towards the edge of the workspace, from (0.25m, 0.144m) to (0.48m, 0.144m) in increments of 1.0 mm is considered. The constant geometric parameters chosen for the manipulator are A,AJ=0.5m and C,C;=0.2m, /1i=/2i=0.2m and D=0°. Fig.2 shows the straight line trajectory and the singular points within the constant orientation workspace of the non-redundant 3-RRR manipulator.\n\nFig. 2 Workspace and straight-line trajectory of 3-RRR linkage\n\n0.25 0.27 0.29 0.31 0.33 0.35 0.37 0.39 0.41 0.43 0.45 0.47 Moving Platform Displacement in x(m)\n\nFig. 3 Actuated torques for the 3-RRR manipulator for the Straight-line trajectory\n\nA constant force of 46.46 N is applied on the platform in the direction opposite to the motion. Fig.3 shows the actuated torques required for the non-redundant manipulator. As can be seen from Fig.2, the manipulator passes through a singularity points from (0.405, 0.144) to (0.48, 0.144). In theory, the joint torques should reach infinity at singularity points. The finite values shown in the Fig.3 are due to the displacement step chosen, which was 1.0 mm. With a finer displacement step, the computation would have failed when the manipulator would have been exactly at the singular configuration. From the plot it is clear that the non-redundant manipulator would not be able to perform the desired trajectory, as it requires infeasible actuated torques at the singular configuration. For the optimization runs of the redundant 3-PRRR manipulator, limits were placed on the displacements of the base prismatic joint. The range of limits on these prismatic joint is from 0.05 m to 0.1 m. In theory, when the position of the actuated joints changes simultaneously the constant-orientation workspace and singularity points are also changes, this range is selected in a way that for all the positions of the prismatic joint the singularity points are falls under the same region where the trajectory is considered as shown in Fig.2.\n\n0.1 0.08 0.06 0.04 0.02 0\n\n0.1 0.08 0.06 0.04 0.02 0\n\n0.1 0.08 0.06 0.04 0.02 0\n\nII n n n n n n n II n n II\n\n0.25 0.27 0.29 0.31 0.33 0.35 0.37 0.39 0.41 Moving Platform Displacement in x (m)\n\n.......\n\nMoving Platform Displacement in x (m)\n\nMoving Platform Displacement in x (m)\n\nFig. 4 Prismatic joints optimum points at minimum torques\n\nFig.4 shows the prismatic joint optimum locations of 1-DOKR, 2-DOKR and 3-DOKR redundant 3-PRRR manipulator respectively where the joint torques are minimum in each time step for the straight line trajectory. And Fig.5 shows the optimized torques for the redundant 3-PRRR manipulator for 1-DOKR and it clearly shows that the joint torques of the redundant manipulator are lower than the non-redundant manipulator. This demonstrates that the actuated torques is being optimized. Comparing Fig.3 with Fig.5, it can be seen that the redundant manipulator easily passes through the singular configuration, while maintaining feasible actuated joint torques. This ability to avoid singular configurations is one of the main advantages of using a redundant manipulator compared to a nonredundant manipulator. Similarly results are showed for 2-DOKR and 3-DOKR in Fig.6. When increasing the degrees of redundancy the actuated joint torques are much minimizing.\n\n0.25 0.27 0.29 0.31 0.33 0.35 0.37 0.39 0.41 0.43 0.45 0.47 Moving Platform Displacement in x (m)\n\nFig. 5 Actuator optimized torques for the 3-PRRR manipulator for the straight-line trajectory\n\nd te at\n\ntu ct Ac\n\n20 5 -10\n\nv_ix>• 1 \"-g\n\n■ t1(2-DOKR)\n\n■ ti(3-DOKR)\n\n0.25 0.27 0.29 0.31 0.33 0.35 0.37 0.39 0.41 0.43 0.45 0.47\n\n0.25 0.27 0.29 0.31 0.33 0.35 0.37 0.39 0.41 0.43 0.45 0.47\n\n----------- -J^^'x 'V ' '.\", '\" ' y\n\n- - - -\n\nT3(2-DOKR) t3(3-DOKR)\n\n0.25 0.27 0.29 0.31 0.33 0.35 0.37 0.39 0.41 0.43 0.45 0.47\n\nMoving Platform Displacement in x (m)\n\nFig. 6 Actuator optimized torques for the 3-PRRR manipulator for the straight-line trajectory\n\n6. Conclusions\n\nIn present formulation, optimized redundant prismatic joint locations of planar 3-PRRR parallel mechanism for obtaining minimum joint torques were obtained. The methodology was illustrated using the system following a straight line trajectory of end-effector. The results indicate that the kinematically-redundant manipulator has improved performance over the non-redundant device. The optimized torques required by the actuators of the redundant manipulator was much lower than those of the non-redundant manipulator. To avoid the complexity of selecting the bounds on prismatic joint variables, the formulation can be extended with dexterity constraints also.\n\nReferences\n\n Kock S, Schumacher W. A parallel x-y manipulator with actuation redundancy for high-speed and active-stiffness applications. Proc. of the IEEE Int Conf on Robotics and Automation 1998; 2295-2300.\n\n Muller A. Internal preload control of redundantly actuated parallel manipulators & its application to backlash avoiding control. IEEE Transactions on Robotics and Automation 2005; 21(4): 668-677.\n\n Ebrahimi I, Carretero JA, Boudreau R. Path Planning for the 3-PRRR Redundant Planar Parallel Manipulator. Proc. of the IFToMM World Congress, Besanc on, France; 2007.\n\n Ebrahimi I, Carretero JA, Boudreau R. Kinematic Analysis and Path Planning of a New Kinematically Redundant Planar Parallel Manipulator. J of Robotica 2008; 26(3): 405-413.\n\n Wang J, Gosselin CM. Kinematic Analysis and Design of Kinematically Redundant Parallel Mechanisms ASME J Mech Des 2004; 126(1): 109-118.\n\n Ebrahimi I, Carretero JA, Boudreau R. 3-PRRR redundant planar parallel manipulator: inverse displacement, workspace and singularity analyses. J Mech and Mach Theory 2007; 42 (8):1007-1016.\n\n Ebrahimi I, Carretero JA, Boudreau R. A Family of Kinematically Redundant Planar Parallel Manipulators J Mech Des 2008; 130: 0623061-8\n\n Cha SH, Lasky TA, Velinsky SA. Kinematically-redundant variations of the 3-RRR mechanism and local optimization-based singularity avoidance. J Mechanics Based Design of Structures and Machines 2007; 35(1): 15-38.\n\n Cha SH, Lasky TA, Velinsky SA. Determination of the kinematically redundant active prismatic joint variable ranges of a planar parallel mechanism for singularity-free trajectories, J Mech and Mach Theory 2009; 44 (5):1032-1044.\n\n Weihmann L, Martins D, Coelho LS. Force capabilities of kinematically redundant planar parallel manipulators. Proc. of the 13th World Congress in Mechanism and Machine Science; 2011.\n\n Boudreau R, Nokleby S. Force optimization of kinematically-redundant planar parallel manipulators following a desired trajectory. J Mech and Mach. Theory 2012; 56: 138-155.\n\n Firmani F, Podhorodeski RP. Singularity Analysis of Planar Parallel Manipulators based on Forward Kinematic Solutions. J Mech Mach Theory 2009; 44: 1386-1399.\n\n Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading, Massachusetts." ]

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[ "A “positive diagonal plus skew-symmetric” matrix decomposition\n\nLet $$A\\in\\mathbb{R}^{n\\times n}$$ be a diagonalizable matrix with real and strictly positive eigenvalues (note that $$A$$ is not required to be symmetric).\n\nMy question. Do there exist an orthogonal matrix $$T\\in\\mathbb{R}^{n\\times n}$$ and a symmetric positive definite matrix $$P\\in\\mathbb{R}^{n\\times n}$$ such that $$TAPT^\\top = D+S,$$ where $$D\\in\\mathbb{R}^{n\\times n}$$ is a diagonal matrix with positive diagonal entries and $$S\\in\\mathbb{R}^{n\\times n}$$ is a skew-symmetric matrix?\n\nOf course, if the diagonal entries of $$D$$ are not required to be positive then the answer is in the affirmative (see, e.g., this related question).\n\n• Question 2 seems trivial - scaling $P$ scales $tr(D)$. – user44191 Sep 25 '18 at 17:24\n• @user44191: Absolutely right! I will remove my second question right away. – Ludwig Sep 25 '18 at 17:27\n\nChoose any positive definite matrix $$Q$$. Since $$A$$ has eigenvalues with positive real part, the Lyapunov equation $$AP + PA^\\top = Q$$ is solvable, and its solution $$P$$ is symmetric and positive definite.\nNow decompose $$AP = H+\\hat{S}$$, where $$H$$ is symmetric and $$\\hat{S}$$ is skew-symmetric. Plugging this decomposition into the Lyapunov equation, we see that $$H=\\frac12 Q$$. Then, take an eigendecomposition $$\\frac12 Q = TDT^\\top$$, with orthogonal $$T$$; since we chose $$Q$$ positive definite, $$D$$ has positive diagonal entries.\nHence we have $$AP = \\frac12 Q + S = TDT^\\top + \\hat{S},$$ with $$\\hat{S}$$ skew-symmetric, or $$T^\\top AP T = D + T^\\top \\hat{S} T,$$ where $$S=T^\\top \\hat{S} T$$ is skew-symmetric.\nRewrite your equation: $$A = (T^{-1} (D+S) T) (T^{-1} P T)$$.\nChoose $$B, C$$ symmetric positive definite with $$A = BC$$ (https://pure.tue.nl/ws/files/1810587/Metis198781.pdf ). Then choose $$D$$ similar to $$B$$, choose $$T$$ such that $$B = T^{-1} D T$$, and $$P = T C T^{-1}$$. Also choose $$S = 0$$." ]

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[ "# The Fourth Dimension Space\n\n## C++中模板使用介绍（转）\n\n1. 模板的概念。\n\n//函数1.\n\nint max(int x,int y);\n{return(x>y)?x:y ;}\n\n//函数2.\nfloat max( float x,float y){\nreturn (x>y)? x:y ;}\n\n//函数3.\ndouble max(double x,double y)\n{return (c>y)? x:y ;}\n\n2.   函数模板的写法\n\nTemplate <class或者也可以用typename T>\n\n{//\n\n//Test.cpp\n\n#include <iostream>\n\nusing std::cout;\n\nusing std::endl;\n\n//声明一个函数模版,用来比较输入的两个相同数据类型的参数的大小，class也可以被typename代替，\n\n//T可以被任何字母或者数字代替。\n\ntemplate <class T>\n\nT min(T x,T y)\n\n{ return(x<y)?x:y;}\n\nvoid main( )\n\n{\n\nint n1=2,n2=10;\n\ndouble d1=1.5,d2=5.6;\n\ncout<< \"较小整数:\"<<min(n1,n2)<<endl;\n\ncout<< \"较小实数:\"<<min(d1,d2)<<endl;\n\nsystem(\"PAUSE\");\n\n}", null, "3. 类模板的写法\n\nTemplate < class或者也可以用typename T >\nclass\n\n／／类定义．．．．．．\n｝；\n\n// ClassTemplate.h\n#ifndef ClassTemplate_HH\n\n#define ClassTemplate_HH\n\ntemplate<typename T1,typename T2>\n\nclass myClass{\n\nprivate:\n\nT1 I;\n\nT2 J;\n\npublic:\n\nmyClass(T1 a, T2 b);//Constructor\n\nvoid show();\n\n};\n\n//这是构造函数\n\n//注意这些格式\n\ntemplate <typename T1,typename T2>\n\nmyClass<T1,T2>::myClass(T1 a,T2 b):I(a),J(b){}\n\n//这是void show();\n\ntemplate <typename T1,typename T2>\n\nvoid myClass<T1,T2>::show()\n\n{\n\ncout<<\"I=\"<<I<<\", J=\"<<J<<endl;\n\n}\n\n#endif\n\n// Test.cpp\n\n#include <iostream>\n\n#include \"ClassTemplate.h\"\n\nusing std::cout;\n\nusing std::endl;\n\nvoid main()\n\n{\n\nmyClass<int,int> class1(3,5);\n\nclass1.show();\n\nmyClass<int,char> class2(3,'a');\n\nclass2.show();\n\nmyClass<double,int> class3(2.9,10);\n\nclass3.show();\n\nsystem(\"PAUSE\");\n\n}", null, "4.非类型模版参数\n\ntemplate<typename T, int MAXSIZE>\n\nclass Stack{\n\nPrivate:\n\nT elems[MAXSIZE];\n\n};\n\nInt main()\n\n{\n\nStack<int, 20> int20Stack;\n\nStack<int, 40> int40Stack;\n\n};\n\nposted on 2009-04-03 11:14 abilitytao 阅读(14398) 评论(16)  编辑 收藏 引用", null, "### 评论\n\n@hexin\n\n#### #re: C++中模板使用详解（转）——写得非常棒，赞~ 2009-04-04 10:03 runsisi\n\nomg，呵呵 确实连模板显示具体化和实例化都没有提哦...被楼主骗了  回复  更多评论\n\n@没事干\n\n@过客\n\n@123456" ]

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[ "# Exporting of Animated gif from polar plot\n\nI want to export an animation(gif type) for polar plot $r=\\cos 2\\theta$ like to the following gif. how can I do it?", null, "rose = Table[PolarPlot[Cos[x i], {i, 0, Pi}, PlotRange -> 1], {x, 0, 10, .1}];\n\nFollowed by:\n\nExport[\"rose.gif\", rose]\n\nWhich gives you the following beautiful animation:", null, "You can change the final number of petals by changing the number 10. You can change the speed of the animation by making the increments smaller than .1.\n\nTo realize the constant-speed drawing, you'll need to re-parameterize the equation to use the arc-length parameter:\n\n$$\\mathrm{d}s = \\left\\| \\frac{\\mathrm{d}\\,\\boldsymbol{\\mathrm{r}}(\\theta)}{\\mathrm{d}\\theta}\\right\\|\\mathrm{d}\\theta$$\n\nr = Cos[2 θ] {Cos[θ], Sin[θ]}\nreParaEq = θ'[s] == 1/FullSimplify[Sqrt[#.#] &@D[r, θ] /. θ -> θ[s]]\nθFunc = DSolveValue[{reParaEq, θ == 0}, θ, s][s]\n(* And the max value of the arc-length: *)\n{sMax} = s /. Solve[θFunc == 2 π, s]\n\n\nTo actually plotting the expected result, we need to turn off MaxRecursion:\n\nwholePlot = ParametricPlot[Evaluate[r /. θ -> θFunc], {s, 0, sMax},\nPlotPoints -> 200, MaxRecursion -> 0\n]\nframes = wholePlot /. ({Line[pts_] :> Line[pts[[;; #]]]} & /@ Range);\n\n\nTo show the animation in Mathematica, we can use ListAnimate:\n\nListAnimate[frames, 60]\n\n\nTo export it as GIF:\n\nExport[\"FourLeaveRose.gif\", frames, \"GIF\", \"DisplayDurations\" -> 1/60, AnimationRepetitions -> ∞]", null, "• To @Silvia Why is your code hard and exotic?!!! Please look at my code in my answer. Dec 1, 2014 at 14:34\n• @bigli It's not exotic at all... just normal differential geometry -- Basically, the so-called natural parameterization walks along the curve with speed proportionally to arc-length $s$, so will force Plot using equally distributed sampled points. (But yes, this effect may not be what you required.) The second benefit of my method would be only invoking Plot once, which is more efficient. Also, I would like to point out the \"DisplayDurations\" option of GIF export, in case it might be handy for you. Dec 1, 2014 at 15:26\n\nBE HAPPY!! The easiest code is:\n\na:=\nShow[PolarPlot[Cos[2 \\[Theta]], {\\[Theta], 0, t}],\nPlotRange -> {{-1, 1}, {-1, 1}}]\nb= ParallelTable[a, {t, 0.001, 2 Pi, (2 Pi - 0.001)/100}];\nExport[\"4-leaved-rose.gif\",b ]\n\n\nand the result is:", null, "• Look at both of them. you should find out difference of them. My answer is just answer of the principal question. Dec 1, 2014 at 14:41\n• You should read Aron's answer more carefully, he shows you how you can write a better code which is even simpler. Another simple one-liner: b = PolarPlot[Cos[2 [Theta]], {\\[Theta], \\$MachineEpsilon, #}, PlotRange -> 1] & /@ Range[0, 2 Pi, 0.02 Pi]; Dec 2, 2014 at 2:39" ]

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[ "Home | Menu | Get Involved | Contact webmaster", null, "", null, "", null, "", null, "", null, "0 / 12\n\n# Number 1847\n\none thousand eight hundred forty seven\n\n### Properties of the number 1847\n\n Factorization 1847 Divisors 1, 1847 Count of divisors 2 Sum of divisors 1848 Previous integer 1846 Next integer 1848 Is prime? YES (283rd prime) Previous prime 1831 Next prime 1861 1847th prime 15823 Is a Fibonacci number? NO Is a Bell number? NO Is a Catalan number? NO Is a factorial? NO Is a regular number? NO Is a perfect number? NO Polygonal number (s < 11)? NO Binary 11100110111 Octal 3467 Duodecimal 109b Hexadecimal 737 Square 3411409 Square root 42.976737893889 Natural logarithm 7.5213179801992 Decimal logarithm 3.2664668954402 Sine -0.25367757416191 Cosine 0.96728883399289 Tangent -0.26225628297056\nNumber 1847 is pronounced one thousand eight hundred forty seven. Number 1847 is a prime number. The prime number before 1847 is 1831. The prime number after 1847 is 1861. Number 1847 has 2 divisors: 1, 1847. Sum of the divisors is 1848. Number 1847 is not a Fibonacci number. It is not a Bell number. Number 1847 is not a Catalan number. Number 1847 is not a regular number (Hamming number). It is a not factorial of any number. Number 1847 is a deficient number and therefore is not a perfect number. Binary numeral for number 1847 is 11100110111. Octal numeral is 3467. Duodecimal value is 109b. Hexadecimal representation is 737. Square of the number 1847 is 3411409. Square root of the number 1847 is 42.976737893889. Natural logarithm of 1847 is 7.5213179801992 Decimal logarithm of the number 1847 is 3.2664668954402 Sine of 1847 is -0.25367757416191. Cosine of the number 1847 is 0.96728883399289. Tangent of the number 1847 is -0.26225628297056\n\n### Number properties\n\n0 / 12\nExamples: 3628800, 9876543211, 12586269025" ]

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[ "The EzyEducation website uses cookies to help ensure we give you the best experience.\nIf you continue without changing your settings, we assume that you are happy to receive all cookies on the EzyEducation website.\n\nContinue\n\n## Countdown to Exams - Day 26 - Fractions - Addition and Subtraction\n\nToday we extend our fraction knowledge and look at calculating with fractions. The focus here will be Addition and Subtraction of fractions. In order to carry out these calculations, the denominators of your fractions need to be the same. This means that you will have to multiply one or both of the fractions to make equivalent fractions that have the same denominator.\n\nRemember to simplify your answers where possible to secure full marks and remember how to convert between mixed and improper fractions.\n\nTags:\n3610 Hits\n\n## Countdown to Exams - Day 3 - Addition and Subtraction\n\nThe focus for Day 3 is Addition and Subtraction. As well as being able to use the appropriate method to add and subtract complex numbers, we explore the rules regarding the addition and subtraction of positive and negative numbers which is often an area where simple marks are lost in an exam.\n\nTags:\n4135 Hits" ]

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[ "# Quantifying robustness of biochemical network models\n\n## Abstract\n\n### Background\n\nRobustness of mathematical models of biochemical networks is important for validation purposes and can be used as a means of selecting between different competing models. Tools for quantifying parametric robustness are needed.\n\n### Results\n\nTwo techniques for describing quantitatively the robustness of an oscillatory model were presented and contrasted. Single-parameter bifurcation analysis was used to evaluate the stability robustness of the limit cycle oscillation as well as the frequency and amplitude of oscillations. A tool from control engineering – the structural singular value (SSV) – was used to quantify robust stability of the limit cycle. Using SSV analysis, we find very poor robustness when the model's parameters are allowed to vary.\n\n### Conclusion\n\nThe results show the usefulness of incorporating SSV analysis to single parameter sensitivity analysis to quantify robustness.\n\n## Background\n\nComplex molecular networks mediate intracellular signalling events. These systems must operate reliably under vastly different environmental conditions that can cause large changes in the internal \"parameters\" of the system. The notion of robustness in biological systems has received considerable interest in the literature recently. By saying that a system is robust we imply that a particular function or characteristic of the system is preserved despite changes in the operating environment of the system. For example, by means of a computer model, Barkai and Leibler demonstrated that the adaptation mechanism found in the chemotactic signalling pathway in Escherichia coli is robust . This was later confirmed experimentally . A model of segment polarity network in Drosophila embryos was also found to be insensitive to variations in kinetic constants that govern its behaviour . A similar approach was later used to show that a core neurogenic network in Drosophila successfully formed three test patterns across a wide range of parameter values leading Meir et al. to propose that the ability to resist parameter fluctuations may be essential for gene network evolutionary flexibility.\n\nSince the signalling pathways are robust, we should expect that mathematical models that attempt to explain these networks also be robust to parameter variations. This has long been appreciated. For example, Savageau, in , argues for parameter sensitivities as a means of evaluating the performance of biochemical systems. More recently, Morohashi et al. propose that robustness of a model to parameter variations be used as a criterion for determining plausibility between different models .\n\nIf we are to use robustness as a means of evaluating the quality of a model, we need objective measures of this robustness. One common technique is through parameter sensitivities. For simple systems, the sensitivity of a model of a network to individual parameters can be evaluated analytically [5, 7]. For more complex networks, it can be determined computationally by repeated simulation varying one parameter while holding all others fixed; [3, 8]. This single parameter sensitivity is also useful for testing robustness of a biochemical network in the laboratory. For example, it is by systematically varying the concentration of the chemotaxis-network proteins in E. coli and determining their effect – or lack thereof – on the precision of adaptation that Alon et al. determined the robustness of this system .\n\nSingle parameter insensitivity is necessary for a robust network, but may not be sufficient owing to interactions between several parameters. This is particularly true in vivo where many different system parameters will differ from their \"nominal\" values simultaneously. The tools available for quantifying this multiparametric uncertainty are more limited. Systematic changes of many parameters at a time suffer from an exponential increase in the number of parameters that need to be changed. This \"curse of dimensionality\" makes varying more than a handful of parameters simultaneously to assess parameter sensitivity impractical. For this reason, sensitivities for several parameters have been traditionally addressed through computer simulations based on Monte Carlo methods – randomly varying all parameter in the model [1, 4]. However, because of their reliance on random methods, Monte Carlo methods cannot guarantee robustness. In this paper we suggest an alternative method, originally developed for use in analysing robust stability in man-made automatic control systems.\n\nThe need for robust systems has been one of the primary concerns of control engineering. In fact, one of the earliest motivations for the study of feedback control systems was the need to create robust telephone networks out of the highly variable vacuum tubes of the day. More recently, powerful tools for analysing the robustness of networks have emerged. In this paper we propose that one of these computational tools, known in control theory as the structural singular value (SSV) is of particular interest for biological networks . We do this by contrasting single and multi-parameter sensitivities of a model of an oscillating biochemical network. We describe this model next.\n\n### Model of an oscillating biochemical network\n\nIn , Laub and Loomis propose a model of the molecular network underlying adenosine 3',5'-cyclic monophosphate (cAMP) oscillations observed in fields of chemotactic Dictyostelium discoideum cells. The model, based on the network depicted in Fig. 1, induces the spontaneous oscillations in cAMP observed during the early development of D. discoideum.\n\nIn this model, changes in the enzymatic activities of these proteins are described by a system of seven non-linear differential equations:", null, "where the state variable x = [x1,...,x7] represents the concentrations of the seven proteins: x1 = [ACA], x2 = [PKA], x3 = [ERK2], x4 = [REG A], x5 = [Internal cAMP], x6 = [External cAMP] and x7 = [CAR1] and the fourteen different k i represent system parameter values. It was shown numerically in that spontaneous oscillations appear at the nominal parameter values found in Table 1. Note that because there are typographical errors in the original paper, the values being used here for the nominal parameters were obtained directly from the authors of .\n\nThis particular model is primarily concerned with describing self-sustaining oscillations in the biochemical system. From Fig. 2, it is clear that at the nominal parameter values of the model, this is achieved. We seek to determine whether the system is robust – that is, if we change these kinetic parameters, will the systems oscillatory behaviour persist? We next present two possible means, based on whether parameters are changed one at a time or in groups.\n\n## Methods\n\n### Single parameter robustness: Bifurcation analysis\n\nSelf-sustained oscillations such as those being modelled here appear as stable limit cycles in trajectory of the underlying dynamical system . The existence and stability of these limit cycles may change under parametric perturbations. Whenever a stable periodic solution loses stability as we vary the underlying parameters of the system and this solution transitions to another qualitative solution – for example, a steady-state equilibrium – we say that the system undergoes a Hopf bifurcation. It is therefore possible to use bifurcation theory as a means of quantifying the robustness of this oscillatory network model [12, 13].\n\nUsing the bifurcation analysis package AUTO , it is possible to produce one-parameter bifurcation diagrams for each of the model parameters k i . These diagrams illustrate the steady-state behaviour of the systems as the parameter values are changed. Suppose that Hopf bifurcations occur at k i and", null, "i so that (stable) limit cycles occur for the range (k i ,", null, "i ). Both the size of this interval as well as the proximity of the nominal parameter value to either boundary are measures of the robustness of the system. To compare the robustness of the system to the different parameters, we can define a series of parametric robustness measures. We define the degree of robustness (DOR) for each parameter k i as:", null, "It is straightforward to see that this value is always between zero and one. The former indicates extreme parameter sensitivity whereas the latter implies large insensitivity.\n\nBifurcation diagrams provide an excellent means of determining the robustness of systems to single parameter perturbations. We next describe a method for analysing and quantifying robustness to simultaneous changes in several parameters.\n\n### Multiparametric robustness: Structural singular values\n\nAs in biological networks, engineering systems must also be robust to variations in the parametric values of its components. Developing tools for the analysis and design of robust automatic control systems has been an area of active research during the last two decades in control theory. One of the most powerful frameworks for measuring robustness known is the structural singular value (SSV) which is due to Doyle and co-workers .\n\nWe first define and illustrate the use of the SSV to quantify robustness by means of a simple example. Suppose that a system is described by the first-order differential equation", null, "= ax\n\nwhere the constant parameter a is uncertain, but is assumed to lie in the region a (a,", null, ").\n\nWe would like to know when this system is robustly stable; that is, it is stable for all possible parameters. The differential equation can be rewritten as", null, "= a0x + b0v     (1)\n\nwhere a0 = (", null, "+ a)/2, b0 = (", null, "- a)/2, v = δx and δ (-1,1). In Eqn. (1), the term a0 represents the nominal system description. Clearly, for the system to be stable we need a0 < 0. The variable δ represents all possible uncertainty in the parameter of the system, whereas b0 dictates the uncertainty's effect on the nominal model. We would like to maintain system stability no matter what the value of δ happens to be. Note that the system can be redrawn in the form of a feedback loop as in Fig. 3A. From the small gain theorem , it is known that if the nominal system is stable (a0 < 0), the uncertain system will remain so whenever the gain around the loop is less than one. That is, if we denote the system transfer function – the ratio of Fourier transforms of output over input – as", null, "(here i refers to the complex number", null, "and ω is the angular frequency) then the system is stable provided that 1 - G(ω)δ ≠ 0, for all frequencies ω. Equivalently, the amount of uncertainty that the system can tolerate is given by", null, "Thus, the function μ = |G(ω)| serves as a (frequency-dependent) measure of the amount of parameter uncertainty that the system can tolerate. In particular, if the size of the uncertainty δ is always less than 1/μ, then the system is robustly stable. In this example, since |δ| < 1, robust stability is guaranteed whenever b0 < |a0|.\n\nIt is clear that this simple model does not require extensive analytic tools to determine robust stability. Nevertheless, the procedure above can be generalized to systems of the form", null, "where A0, is a matrix describing the nominal model, B0, C0, and D0 are matrices of appropriate dimensions describing the way that the uncertain parameters affect the nominal model. This uncertainty is modelled by the matrix Δ which is unknown, but is assumed to belong to the set", null, ". The signal u = Δy completes the feedback loop as shown in Fig. 3B. For these systems, the appropriate measure of robustness is now given by the structural singular value (SSV)\n\nμΔ (G) = (min{||Δ||:Δ", null, ", det(I - G Δ) ≠ 0})-1     (3)\n\nHere, G(ω) = C0 (iωI - A0)-1 B0 + D0 and I is the identity matrix of appropriate dimensions.\n\nSince we are interested in the robustness of the oscillatory property of this system, it is natural to use the SSV to quantify the robust stability of the limit cycle. However, in order to use the SSV tool, the original perturbed system must be transformed into a framework consisting of a nominal linear time invariant (LTI) system interconnected with a perturbation matrix. For the case of an oscillatory non-linear model, this involves several steps, which we outline next.\n\n#### Determining the limit cycle: Harmonic balance method\n\nThe first step is to obtain a mathematical expression for the limit cycle oscillation. The harmonic balance method can be used . The basic idea is to represent the limit cycle by a Fourier series with unknown coefficients (an,i, φn,i) and period T:", null, "The non-linear differential equation can be used to set up a series of algebraic equations that the coefficients must satisfy. These equations can be solved using numerical packages such as Mathematica or Maple. Depending on the particular form of the limit cycle, a small finite number of coefficients can be used. We can denote this periodic solution as x*(t).\n\n#### Linearization\n\nThe non-linear differential equation must now be linearized about this periodic orbit . Writing the state vector x(t) as\n\nx(t) = x*(t) + xδ (t)\n\nthen the local behaviour of the non-linear system is governed by that of the linearized system:", null, "δ (t) J (x*(t))x (t)\n\nwhere J is the Jacobian matrix of the vector field f. Note that since the linearization is performed about a periodic orbit, the linear system is periodic.\n\n#### Restructuring into nominal/uncertainty systems\n\nThe Jacobian matrix includes all uncertain parameters. At this point we need to separate the system into a nominal model and a feedback interconnection that involves all parametric uncertainty. We first write each parameter as", null, "where k i is the nominal value and δ i is the relative amount of perturbation in the ith parameter. We now separate the Jacobian matrix as\n\nJ (x*(t)) = A0 (t) + B0 (t) Δ C0 (t)     (4)\n\nwhere A0(t) is the Jacobian matrix with all parameters at their nominal value, and Δ is a diagonal matrix containing all the uncertainties δ i . Let y(t) = C0(t) xδ(t) and u(t) = Δy(t), the system is now of the form of Eqn. (2) (with x(t) replaced by xδ(t)).\n\n#### Discretization\n\nThe system can be discretized by sampling the state and output with sampling period h = T/n, where n is a positive integer and assuming that the inputs are piecewise constant; this is also a standard technique in control engineering . In particular, a linear continuous-time system governed by Eqn. (2) gives rise to the discrete-time, linear system\n\nξ (k + 1) = A d (k) ξ(k) + B d (k) v(k)\n\nη (k) = C d (k) ξ(k)\n\nwhere A d (k) = Φ (kh + h,kh), B d (k) =", null, "Φ (kh + h, s) B0 (s)ds, C d (k) = C0 (kh), and Φ (t, τ) is the transition matrix of A0 (t) . The discretized signals are v(k) = u(kh), η(k) = y(kh), and ξ(k) = x(kh). Periodicity of A d and B d is preserved due to the periodicity of the transition matrix. Moreover, it is not difficult to confirm that A d , B d and C d are periodic with period n. The uncertainty matrix after discretization is now Δ d . The discretization step is illustrated in Fig. 4A.\n\n#### Lifting\n\nThe final step in preparing the system for SSV analysis is to transform the periodic, linearized system into an equivalent time-invariant one. The technique for this is known as lifting . Rather than giving the general formulae, it is easier to illustrate the general principle with an example.\n\nSuppose that a discrete-time system with state variable ξ, input v, and output η obeys the difference equation\n\nξ (k + 1) = a(k)ξ(k) + b(k)v(k)\n\nη (k) = c(k)ξ(k)\n\nwhere the time varying coefficients a(k), b(k) and c(k) are all periodic with period two. Calculating the state variable and output step-by-step leads to:", null, "for any integer p. By defining \"lifted\" inputs and outputs", null, "and considering the system state only at the even time points (", null, "(p) = ξ(2p)) we arrive at an equivalent time-invariant system.\n\nThe lifting technique has been illustrated above for a discrete-time system with period two; however, it can be applied to systems with arbitrary period – though the corresponding formulae are considerably more complicated; see .\n\n#### Computation of SSV\n\nThere is considerable literature in control theory on the computation of the SSV; see for example . For general classes of uncertainty, computing μΔ is known to be NP-hard . Typically, given the feedback loop consisting of G and Δ we compute upper and lower bounds for the SSV . The lower bound is exactly equal to μΔ ; unfortunately computing this lower bound involves a search over a non-convex set and therefore may converge to local optimums that are not global. In contrast, the upper bound can be rewritten in terms of a convex optimisation problem, so that a global minimum can be obtained. However, this upper bound is, in general not tight. A software package is commercially available that can compute μupperand uses a power algorithm to attempt to compute μlower.\n\n## Results\n\n### Single parameter robustness\n\nThe robustness of Laub and Loomis's oscillatory model was first analysed by means of single-parameter bifurcation diagrams. Four typical diagrams are shown in Fig. 5. The activity of internal cAMP (x5) is plotted as a function of the variation of each parameter. We use internal cAMP in the diagram as it is the element that is usually observed experimentally . In each of the diagrams, there are three types of solutions: stable steady state, unstable steady state and limit cycle oscillations.\n\nThese diagrams illustrate that Hopf bifurcations occur for each parameter; that is, the oscillatory behaviour exists only in a limited range of parameters around the nominal value. For each of these parameters, the respective intervals and values for degree-of-robustness are found in Table 1.\n\n### Structural singular value\n\nFrom the numerical simulation (Fig. 2) of the non-linear model, we observed that the oscillatory curves did not deviate greatly from a simple harmonic oscillator plus a constant offset. Thus, to obtain an analytic expression for the periodic orbits we assume that the state variables are expanded into Fourier series containing only the fundamental and constant terms:", null, "for each of the seven states. Since it is the relative phase shift between each state variable that is relevant, we assume that θ1 = 0. The substitution of the Fourier series into the original equations leads to a series of real algebraic equations for the coefficients (not shown) whose solution was obtained using Mathematica. This leads us to obtain the corresponding periodic solutions where the values of A0,i, A1,iand θ i are found in Table 2. The period T is approximately 7.31 minutes. This analytic solution matches well with the numerical simulation except for an arbitrary phase shift, which does not affect the shape and location of the limit cycle in the phase space and can thereby be ignored (not shown).\n\nFollowing our prescribed methods, we next linearized the system. The Jacobian matrix is obtained and was decomposed as in Eqn. (4) to obtain:", null, "The matrix B0 (t) = {Bi,j} where", null, "Similarly, the matrix C0 (t) = {Ci,j} where all coefficients are zero except for the following:", null, "Finally, D0 = 0 and the perturbation structure is given by\n\nΔ = diag {δ12234566889101011121314}\n\nNote that since the nominal trajectory is periodic, the matrix functions in the nominal description are also periodic. Note also that in the uncertainty matrix, Δ, some uncertainties are repeated (δ268 and δ10) while δ7 is missing.\n\nThe system was then discretized and lifted following the procedure outlined above. A comparison of the system response for each of the approximations at the nominal parameter values is given in Fig. 4B.\n\nFor the sampling time we tried various values of n but found negligible differences for values above eight. Finally, we computed the bounds on the SSV. Once again, we found that the values of these two bounds were not affected much by the sampling frequency provided that n is greater than eight. The upper bound was successfully computed using . The maximum over all frequencies is approximately 12.06. However, the high dimension of system causes convergence problem during the computation of μlowerusing this package. To obtain an acceptable lower bound, we calculate the spectral radius at each frequency. This gives us a lower bound for μlower. The plot of the bounds for the SSV when n = 16 is shown in Fig. 6. We can use μlowerto obtain a conservative region for robust stability. The highest value over all frequencies for μloweris approximately 2.636.\n\n## Discussion\n\nRecent years has seen an appreciation that key cellular properties are robust to variations in individual parameter values. Based on the topology of many of these networks, this should not be surprising. Feedback – both negative and positive – control systems are ubiquitous in most biological networks and one of the reasons for using feedback is that it reduces sensitivity of a system's behaviour to its parameter values.\n\nIn modelling biological networks, it is important that this robustness also be in evidence. The particular behaviour being characterized by the model should not rely on precise values of the model's parameters – for example, reaction rate constants or protein concentrations. In particular, a precise measurement of these constants is difficult whereas protein concentrations will vary from one cell to another or throughout the lifetime of any individual. Deviations from the nominal model parameter values should not result in a loss of the network's performance; thus, parameter sensitivity can be used to validate mathematical models of biochemical system. That is, the more insensitive the system response is to the accuracy of the parameter, the more faith we should have in the model .\n\nIn looking at certain classes of behaviour, where qualitative changes in the stability of the system are possible, bifurcation diagrams provide an elegant means of evaluating robustness. For example, in evaluating the robustness of the model of Laub and Loomis, of primary importance is determining whether the oscillatory behaviour will persist if the parameter values are altered. This qualitative difference in performance – from limit cycle oscillations to constant steady states – can be quantified and compared across parameters or from one model to another. Once the robustness of the oscillatory behaviour is established, further investigations of the robustness of some of the oscillatory features, for example frequency and amplitude can further be evaluated.\n\nFrom the bifurcation diagrams obtained for each of the fourteen parameters, we know that oscillations exist only in a limited range around the nominal value. We find the system to be quite sensitive to variations in k2, k4, k10 and k14 and mostly insensitive to the others. Single-parameter bifurcation analysis also shows that the amplitude of the oscillation is greatly affected by the variation of 9 parameters (k1, k2, k4, k6, k7, k10, k11, k12, and k14).\n\nBased on the SSV stability to interpret multiple parameter sensitivity, we can conclude that robust stability of the periodic orbits will be maintained, provided that", null, "Since the uncertainty matrix consists only of diagonal entries, this bound applies to each of the individual parameters. Thus, we can guarantee that the system will be robustly stable provided that no single parameter differs more than 8.3% from its nominal value.\n\nIn our analysis we found a large gap between μupperand our lower bound for μ. As we later show, for this system the upper bound is fairly tight, as we are able to obtain a destabilizing perturbation of size 9%. For general biological models, a robustness measure based on the upper bound μuppermay also be more appropriate. Robustness bounds for systems in which arbitrarily slowly-time-varying parameter values are allowed are known . For these systems it has been shown that the bounds converge as the time-variations approach zero to the upper bound μupper. Since many of the parameters in models of biochemical networks represent features that will vary over time, such as enzyme concentrations, this number may therefore be more indicative of the model's true robustness.\n\nThe ability to consider the effect of time-variations on the robustness of the system is one great advantage of the SSV over other methodologies. One drawback of the SSV approach compared to the bifurcation theory is that it does not provide the precise combination of parameters that destabilizes the system – only its size. Also, since the upper bound is only sufficient to guarantee robustness, this number may, in general, give an overly conservative notion of robustness.\n\nIt must be emphasized that the SSV approach denoted here is based on the linearized model of the system. For some classes of systems this linearization may not be possible – in this case, the linear SSV approach documented here will not be applicable. However, for most models used to describe biochemical reactions, this should not be a problem.\n\nBecause we are concentrating exclusively on the local stability of the linearized model, important parameters of the oscillatory behaviour such as robustness of the frequency and amplitudes of oscillation are not evaluated. Also, the effect of parameter variations on the equilibrium orbit are omitted. In particular, varying the kinetic parameters will change the behaviour of the system in two different ways: the equilibrium periodic orbit will change and the stability of deviations about this orbit will also change. The SSV allows one to quantify the robustness of the second of these two effects. It does not say anything directly regarding the effect of parameter variations on the equilibrium periodic orbit. One way of bounding the effect of these parameter changes is to write the original differential equation as", null, "(t) = f(x,k)\n\nwhere k = k0 + δ is the set of kinetic parameters with nominal values k0. If the nominal periodic orbit (when δ = 0) is given by\n\nx*(t) = x(t) - xδ (t)", null, "δ(t) = A(t)xδ (t) + v\n\nwhere", null, "δ is a constant vector that includes the effect of this parametric uncertainty. Thus, the system can be considered as being perturbed by a constant input signal v. Provided that the homogeneous system is exponentially stable (and this is guaranteed by the existence of a stable limit cycle) and that v is not \"too large\", the perturbed system's state will remain in a neighbourhood of the origin if the f(x,p) in the original equation is reasonably well behaved in k. Detailed bounds and conditions on f are given in Theorem 5.1 of , though it should be emphasized that these bounds tend to be overly conservative in practice.\n\nTo illustrate the local nature of the SSV analysis for this system, we perturbed the system parameters by varying amounts. The particular parameters were either increased or decreased so as to bring them closer to the Hopf bifurcation. For example, the nominal value of k1 is closer to k1 than to", null, "1 so that we reduced k1 whereas k4 is closer to", null, "4 than to k4 so we increased k4. In Fig. 7 we show the response of these systems to changes of 7% and 9% both for the linearized system – where the linearized response has been superimposed on the nominal limit cycle (Fig. 7A) and the original non-linear system (Fig. 7B). For the smaller value, the linearized response is stable and we see that, after a transient, the response settles to the nominal limit cycle. We also see this same behaviour in the response of the non-linear system with this level of parameter perturbation. For a 9% change in the parameters, however, the linearized system is unstable. We see this as a deviation from the nominal limit cycle. In the non-linear system's response, this translates into an end to the stable limit cycle. The response does not \"blow up\" but instead settles into a fixed point.\n\nThis example illustrates how a robustness analysis of the linearized system can be used to deduce the robustness of the original non-linear system, as it shows that when the linearized system is unstable, the desired behaviour of the non-linear system will no longer be present. This example also points out the fact that the upper bound μupper 8.3% is not overly conservative for this system as we were able to produce a destabilizing perturbation of size 9%.\n\nFinally, we note that multiparametric robustness analysis considered here is based on local properties of the dynamical system, since we are evaluating the robustness of the linearized model. Extensions to the non-linear model are the subject of active investigation .\n\nHowever, it is by combining the robustness analysis of both single and multiple parameters, we can obtain a more thorough understanding of the region of stability of the periodic solution in the high dimensional parameter space and use this to improve upon the model. In this particular example, we find that the system's robustness is governed by several \"robustness limiting\" parameters, k2, k4, k10 and k14.\n\n## Conclusions\n\nDetermining the robustness of mathematical models of biological systems is important for several reasons. First, there is growing evidence that many aspects of the networks being modelled have evolved in such a way so that they are robust as this allows them to tolerate natural variations in the environment. Thus, faithful models should replicate this robustness. Second, robustness of the models provide a means of validating model quality since the performance of the models should not rely on precisely tuned parameter values that are impossible – or at best – difficult to measure exactly.\n\nIn this paper, we illustrated the use of two tools developed in dynamical systems theory and control engineering to assess robustness quantitatively. For an example, we considered an oscillatory molecular network model due to Laub and Loomis that aims at describing oscillatory behaviour in cAMP signalling observed in the social amoeba D. discoideum. This behaviour appears as a stable limit cycle of the equations describing the model. We have evaluated the degree to which this limit cycle is robust to variations in all the system parameters.\n\nThe robustness of the oscillatory behaviour to single parameter variations was quantified using bifurcation analysis. Using the bifurcation analysis software tool AUTO we determined that single parameter changes as small as 20% from the nominal value can cause the limit cycle to disappear and a stable equilibrium to appear. In addition to the stability robustness, AUTO is also able to evaluate the sensitivity of the amplitude of the oscillation to these parameter changes.\n\nTo investigate the robustness of the model to simultaneous changes in parameter values, the structured singular value (SSV) analysis tool was used. Once the system was in the correct framework for SSV analysis, we were able to determine that the system can only tolerate very small changes in the parameter values – in the order of 8% – if we allow these parameters to vary with time arbitrarily slowly.\n\nFinally, it is important to note that to understand completely the robustness properties of a model, it is appropriate to combine single and multiple parameter sensitivity analyses.\n\n## References\n\n1. 1.\n\nBarkai N, Leibler S: Robustness in simple biochemical networks. Nature 1997, 387: 913–917. 10.1038/43199\n\n2. 2.\n\nAlon U, Surette MG, Barkai N, Leibler S: Robustness in bacterial chemotaxis. Nature 1999, 397: 168–171. 10.1038/16483\n\n3. 3.\n\nvon Dassow G, Meir E, Munro EM, Odell GM: The segment polarity network is a robust developmental module. 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IEE Proceedings-D Control Theory and Applications 1982, 129: 242–250.\n\n16. 16.\n\nZames G: On input-output stability of time-varying nonlinear feedback systems, I: Conditions derived using concepts of loop gain conicity and positivity. IEEE Transactions on Automatic Control 1966, AC11: 228–238.\n\n17. 17.\n\nKhalil HK: Nonlinear systems 3 Edition Englewood Cliffs, NJ: Prentice Hall 2002.\n\n18. 18.\n\nChen T, Francis BA: Optimal sampled-data control systems London: Springer-Verlag 1995.\n\n19. 19.\n\nRugh WJ: Linear system theory Englewood Cliffs, NJ: Prentice-Hall 1996.\n\n20. 20.\n\nQiu L, Bernhardsson B, Rantzer A, Davison EJ, Young PM, Doyle JC: A formula for computation of the real stability radius. Automatica 1995, 31: 879–890. 10.1016/0005-1098(95)00024-Q\n\n21. 21.\n\nBraatz RP, Young PM, Doyle JC, Morari M: Computational-complexity of μ-calculation. IEEE Transactions on Automatic Control 1994, 39: 1000–1002. 10.1109/9.284879\n\n22. 22.\n\nBalas GJ, Doyle JC, Glover K, Packard A, Smith R: μ-analysis and synthesis toolbox (Mu-Tools). Automatica 1994, 30: 733–735. 10.1016/0005-1098(94)90164-3\n\n23. 23.\n\nGerisch G, Wick U: Intracellular oscillations and release of cyclic AMP from Dictyostelium cells. Biochem Biophys Res Commun 1975, 65: 364–370.\n\n24. 24.\n\nFreeman M: Feedback control of intercellular signalling in development. Nature 2000, 408: 313–319. 10.1038/35042500\n\n25. 25.\n\nHaefner JW: Modeling biological systems: Principles and applications New York: Chapman and Hall 1996.\n\n26. 26.\n\nJönsson U, Rantzer A: Systems with uncertain parameters – time-variations with bounded derivatives. Internat J Robust Nonlinear Control 1996, 6: 969–982. Publisher Full Text 10.1002/(SICI)1099-1239(199611)6:9/10%3C969::AID-RNC262%3E3.3.CO;2-R\n\n27. 27.\n\nParrilo PA: Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization Pasadena, CA: California Institute of Technology 2000.\n\n## Acknowledgements\n\nWe thank J. Krishnan and W.J. Rugh for useful comments on the manuscript. This work was supported in part by the Whitaker Foundation and the National Science Foundation's Biocomplexity program, through grant number DMS-0083500.\n\n## Author information\n\nAuthors\n\n### Corresponding author\n\nCorrespondence to Pablo A Iglesias.\n\n### Authors' contributions\n\nLM carried out the computational studies and analysis. PAI conceived of the study and participated in its design and coordination. All authors read and approved the final manuscript.\n\n## Authors’ original submitted files for images\n\nBelow are the links to the authors’ original submitted files for images.\n\n## Rights and permissions\n\nReprints and Permissions\n\nMa, L., Iglesias, P.A. Quantifying robustness of biochemical network models. BMC Bioinformatics 3, 38 (2002). https://0-doi-org.brum.beds.ac.uk/10.1186/1471-2105-3-38", null, "" ]

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[ "", null, "Tweet\n\n# Excel Workbook and Worksheet Objects Tutorial\n\nIn this lesson we will tell you what the Objects in Excel Visual Basic Application are.\n\n## Introduction and Hierarchy of Objects\n\nAn object is instance of something that hold some properties. Like John is object of Human, which hold many common properties that most humans have. In Excel one object can contain another object, than further that object can contain another object.\n\nExcel VBA Programming involves working with an object hierarchy. It might sound quite confusing but in till the end of this lesson you will fairly familiar with what objects are and how they work in Excel VBA.\n\nIn Excel, we can say parent of all objects is Excel itself, and we call it Application object. Application object contains other objects, for example, the workbook object (this can be any workbook you have created). The workbook object can contain other objects, such as the worksheet object. The worksheet object contains other objects such as range object.\n\nWe hope you have already know that how to create a Macro in Excel if not then please check our tutorial on How to Create a Macro. In that chapter we have shown how to run code by clicking on command button. We used the following line of code in that chapter.\n\nRange(\"A1\").Value = \"Hello\"\n\nLet me elaborate that line for you. Range is and object and Value is its property, we are assigning a string value “Hello” to object. This Range object is Child of its parent object, let’s see full hierarchy.\n\nApplication.Workbooks(\"create-a-macro\").Worksheets(1).Range(\"A1\").Value = \"Hello\"\n\nYou can clearly understand now, that Application is an object and it is accessing its child object Workbooks and in brackets (“create-a-macro”) is name of workbook it is accessing.\n\nNow Workbook object is accessing its child object Worksheets and passing worksheet number in brackets (1), now Worksheet object is further accessing Range object that is child of it.\n\n## What are the Collections\n\nYou have noticed that workbooks and worksheets both are plural, but why? Because they are collections. Workbooks collection contains all the workbook objects that are currently open. The worksheet collection contains all the worksheet objects in a workbook.\n\n## How to refer to member of a collection\n\nYou can refer any member of any collection by following three methods.\n\n1. Using the worksheet name.\n\nWorksheets(\"Sales\").Range(\"A1\").Value = \"Hello\"\n\n2. Using the index number (1 is the first worksheet starting from the left)\n\nWorksheets(1).Range(\"A1\").Value = \"Hello\"\n\n3. Using the CodeName.\n\nSheet1.Range(\"A1\").Value = \"Hello\"\n\nNote: to see CodeName of any workseet, open the Visual basic editor. You can access VB Editor by clicking on Developer tab.\n\nIn project Explorer, the first name is Codename and second name is the worksheet’s name.", null, "In image above you can see Sheet1 is CodeName and mySheet in actual name of worksheet.\n\nReferencing a worksheet using codename is safest way to refer any worksheet because CodeName always remains the same even if you change name of worksheet.\n\nBut if you want to refer any worksheet into another workbook this method will not work.\n\n## Properties and Methods\n\nNow we will learn about some properties and methods of Workbooks and Worksheets collection. Properties are something which a collections holds and which describe that collection, while methods can perform some action with a collection.\n\nWe have already added a command button in our previous lesson, now we will perform some actions with that. Open VB Editor and write following line of code\n\nThis Add method will create new Workbook. If we use it like following\n\nIt will add new worksheet to collection of worksheets.\n\nThe Count property of the Worksheets collection counts the number of worksheets in a workbook. Write the following line in code.\n\nMsgBox Worksheets.Count\n\nNow close VB Editor to try if your applied property of method works, click on button. In our example we have applied Add Method for worksheets.", null, "After clicking on Command button, a new worksheet will added.\n\nThis is how we can use Methods and Properties.", null, "", null, "", null, "", null, "" ]

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[ "", null, "#jsDisabledContent { display:none; } My Account |  Register |  Help", null, "Flag as Inappropriate", null, "This article will be permanently flagged as inappropriate and made unaccessible to everyone. Are you certain this article is inappropriate?          Excessive Violence          Sexual Content          Political / Social Email this Article Email Address:\n\n# Correlation function\n\nArticle Id: WHEBN0000294927\nReproduction Date:\n\n Title: Correlation function", null, "Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:\n\n### Correlation function\n\nA correlation function is a statistical correlation between random variables at two different points in space or time, usually as a function of the spatial or temporal distance between the points. If one considers the correlation function between random variables representing the same quantity measured at two different points then this is often referred to as an autocorrelation function being made up of autocorrelations. Correlation functions of different random variables are sometimes called cross correlation functions to emphasise that different variables are being considered and because they are made up of cross correlations.\n\nCorrelation functions are a useful indicator of dependencies as a function of distance in time or space, and they can be used to assess the distance required between sample points for the values to be effectively uncorrelated. In addition, they can form the basis of rules for interpolating values at points for which there are no observations.\n\nCorrelation functions used in astronomy, financial analysis, and statistical mechanics differ only in the particular stochastic processes they are applied to. In quantum field theory there are correlation functions over quantum distributions.\n\n## Definition\n\nFor random variables X(s) and X(t) at different points s and t of some space, the correlation function is\n\nC(s,t) = \\operatorname{corr} ( X(s), X(t) ) ,\n\nwhere \\operatorname{corr} is described in the article on correlation. In this definition, it has been assumed that the stochastic variable is scalar-valued. If it is not, then more complicated correlation functions can be defined. For example, if X(s) is a vector, then a matrix of correlation functions is defined as\n\nC_{ij}(s,t) = \\operatorname{corr}( X_i(s), X_j(t) )\n\nor a scalar, which is the trace of this matrix. If the probability distribution has any target space symmetries, i.e. symmetries in the value space of the stochastic variable (also called internal symmetries), then the correlation matrix will have induced symmetries. Similarly, if there are symmetries of the space (or time) domain in which the random variables exist (also called spacetime symmetries), then the correlation function will have corresponding space or time symmetries. Examples of important spacetime symmetries are —\n\n• translational symmetry yields C(s,s') = C(s − s') where s and s' are to be interpreted as vectors giving coordinates of the points\n• rotational symmetry in addition to the above gives C(s, s') = C(|s − s'|) where |x| denotes the norm of the vector x (for actual rotations this is the Euclidean or 2-norm).\n\nHigher order correlation functions are often defined. A typical correlation function of order n is\n\nC_{i_1i_2\\cdots i_n}(s_1,s_2,\\cdots,s_n) = \\langle X_{i_1}(s_1) X_{i_2}(s_2) \\cdots X_{i_n}(s_n)\\rangle.\n\nIf the random variable has only one component, then the indices i_j are redundant. If there are symmetries, then the correlation function can be broken up into irreducible representations of the symmetries — both internal and spacetime.\n\nThe case of correlations of a single random variable can be thought of as a special case of autocorrelation of a stochastic process on a space which contains a single point.\n\n## Properties of probability distributions\n\nWith these definitions, the study of correlation functions is similar to the study of probability distributions. Many stochastic processes can be completely characterized by their correlation functions; the most notable example is the class of Gaussian processes.\n\nProbability distributions defined on a finite number of points can always be normalized, but when these are defined over continuous spaces, then extra care is called for. The study of such distributions started with the study of random walks and led to the notion of the Itō calculus.\n\nThe Feynman path integral in Euclidean space generalizes this to other problems of interest to statistical mechanics. Any probability distribution which obeys a condition on correlation functions called reflection positivity lead to a local quantum field theory after Wick rotation to Minkowski spacetime. The operation of renormalization is a specified set of mappings from the space of probability distributions to itself. A quantum field theory is called renormalizable if this mapping has a fixed point which gives a quantum field theory." ]

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[ "", null, "ISBN-10: 0849387078\n\nISBN-13: 9780849387074\n\nISBN-10: 1584881623\n\nISBN-13: 9781584881629\n\nISBN-10: 1584881631\n\nISBN-13: 9781584881636\n\nEven if the research of scattering for closed our bodies of straightforward geometric form is easily constructed, constructions with edges, cavities, or inclusions have appeared, beforehand, intractable to analytical tools. This two-volume set describes a leap forward in analytical thoughts for properly selecting diffraction from sessions of canonical scatterers with comprising edges and different complicated hollow space positive aspects. it's an authoritative account of mathematical advancements over the past 20 years that offers benchmarks opposed to which options acquired by means of numerical tools will be verified.The first quantity, Canonical constructions in power concept, develops the maths, fixing combined boundary capability difficulties for buildings with cavities and edges. the second one quantity, Acoustic and Electromagnetic Diffraction by way of Canonical buildings, examines the diffraction of acoustic and electromagnetic waves from a number of sessions of open buildings with edges or cavities. jointly those volumes current an authoritative and unified remedy of strength concept and diffraction-the first entire description quantifying the scattering mechanisms in advanced buildings.\n\nSimilar functional analysis books\n\nRead e-book online A Course in Functional Analysis PDF\n\nThis booklet is an introductory textual content in useful research. not like many sleek remedies, it starts with the actual and works its technique to the extra common. From the studies: \"This e-book is a superb textual content for a primary graduate direction in sensible research. .. .Many attention-grabbing and demanding functions are incorporated.\n\nGet Current Topics in Pure and Computational Complex Analysis PDF\n\nThe booklet comprises thirteen articles, a few of that are survey articles and others learn papers. Written by way of eminent mathematicians, those articles have been provided on the foreign Workshop on advanced research and Its functions held at Walchand collage of Engineering, Sangli. the entire contributing authors are actively engaged in study fields relating to the subject of the e-book.\n\nThis can be an routines publication firstly graduate point, whose objective is to demonstrate the various connections among sensible research and the speculation of capabilities of 1 variable. A key position is performed by means of the notions of optimistic yes kernel and of reproducing kernel Hilbert area. a couple of evidence from sensible research and topological vector areas are surveyed.\n\nAdditional resources for Canonical problems in scattering and potential theory\n\nExample text\n\n203) to determine that {Er , Hr } = − 1 1 ∂ dr sin θ ∂θ i 1 4π kd2 r2 sin θ ∂G3 ∂θ = ∞ n (n + 1) (2n + 1) n=1 ζn (kd) ψn (kr) , r < d ψn (kd) ζn (kr) , r > d Pn (cos θ) . (1. 219) The orthogonality of Legendre polynomials on (0, π) implies that {an , bn } = − i 1 (2n + 1) 4π kd2 so that (U, V ) = i 1 4π ikd2 r ∞ (2n + 1) n=1 ζn (kd) ψn (kr) , r < d ψn (kd) ζn (kr) , r > d Pn (cos θ) . (1. 220) The electromagnetic field components radiated by a vertical electric or magnetic dipole are comparatively easy to derive.\n\n259) Thus the normal derivative is continuous across the aperture, but there is a discontinuity in its value in moving from the interior to the exterior through a point on S0 (or Γ0 ). The formulation of the electromagnetic boundary conditions is as follows. 4) the boundary surface S (or contour Γ) separates two media with different electromagnetic parameters ε1 , µ1 , σ1 , → − − → and ε2 , µ2 , σ1 ; denote the corresponding electromagnetic fields by E 1 , H 1 → − − → and E 2 , H 2 , respectively.\n\nR r ∂θ (1. 207) To transform (1. 207) we need the partial derivatives ∂G3 1 ikR − 1 ikR e (r − d cos θ) , = ∂r 4π R3 ∂G3 1 ikR − 1 ikR e dr sin θ, = ∂θ 4π R3 ∂G3 1 ikR − 1 ikR e (d − r cos θ) , = ∂d 4π R3 (1. 208) from which it follows that sin θ ∂G3 cos θ ∂G3 1 ∂G3 + = , ∂r r ∂θ d ∂θ ∂G3 sin θ ∂G3 ∂G3 + cos θ = , ∂r ∂d d ∂θ sin θ ∂G3 ∂G3 ∂G3 − cos θ = . d ∂θ ∂d ∂r Taking into account (1. 209), equation (1. 207) becomes Hφ Eφ = ik −ik 1 ∂G3 , d ∂θ (1. 209) (1. 210) (1. 211) (1. 212) and using equation (1." ]

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[ "## Bayesian multilevel modeling: Nonlinear, joint, SEM-like\n\nMultilevel models are used by many disciplines to model group-specific effects, which may arise at different levels of hierarchy. Think of regions, states nested within regions, and companies nested within states within regions. Or think hospitals, doctors nested within hospitals, and patients nested within doctors nested within hospitals.\n\nIn addition to the standard benefits of Bayesian analysis, Bayesian multilevel modeling offers many advantages for data with a small number of groups or panels. And it provides principled ways to compare effects across different groups by using posterior distributions of the effects. See more discussion here.\n\nbayesmh has a new random-effects syntax that makes it easy to fit Bayesian multilevel models. And it opens the door to fitting new classes of multilevel models. You can fit univariate linear and nonlinear multilevel models more easily. And you can now fit multivariate linear and nonlinear multilevel models!\n\nThink of mixed-effects nonlinear models as fit by menl, or some SEM models as fit by sem and gsem, or multivariate nonlinear models that contain random effects and, as of now, cannot be fit by any existing Stata command. You can now fit Bayesian counterparts of these models and more by using bayesmh.\n\n## Let’s see it work\n\nTwo-level models\n\nNonlinear multilevel models\n\nSEM-type models\n\nJoint models of longitudinal and survival data\n\nMultivariate nonlinear growth models\n\n## Two-level models\n\nLet’s start simple and fit a few two-level models first.\n\nSee Bayesian multilevel models using the bayes prefix. There, we show how to use bayes: mixed and other bayes multilevel commands to fit Bayesian multilevel models. Let’s replicate some of the specifications here using the new random-effects syntax of bayesmh.\n\nWe consider the same data on math scores of pupils in the third and fifth years from different schools in Inner London (Mortimore et al. 1988). We want to investigate a school effect on math scores.\n\nLet’s fit a simple two-level random-intercept model to these data using bayesmh. We specify the random intercepts at the school level as U0[school] and include them in the regression specification.\n\nbayesmh requires prior specifications for all parameters except random effects. For random effects, it assumes a normal prior distribution with mean 0 and variance component {var_U0}, where U0 is the name of the random effect. But we must specify the prior for {var_U0}. We specify normal priors with mean 0 and variance 10,000 for the regression coefficients and an inverse-gamma prior with shape and scale of 0.01 for variance components. We specify a seed for reproducibility and use a smaller MCMC size of 1,000.", null, "The results are similar to those from bayes: mixed in Random intercepts. We could replicate the same postestimation analysis from that section after bayesmh, including the display and graphs of random effects. In addition to the main model parameters, Bayesian models also estimate all random effects. This is in contrast with the frequentist analysis, where random effects are not estimated jointly with model parameters but are predicted after estimation conditional on model parameters.\n\nNext we include random coefficients for math as c.math3#U1[school]. We additionally need to specify a prior for the variance component {var_U1}. We added to the variance-components list using the inverse-gamma prior.", null, "Our results are similar to those from bayes: mixed in Random coefficients.\n\nBy default, bayesmh assumes that random effects U0[id] and U1[id] are independent a priori. But we can modify this by specifying a multivariate normal distribution for them with an unstructured covariance matrix {Sigma,m}. We additionally specify an inverse Wishart prior for the covariance {Sigma,m}.", null, "The results are again similar to those from bayes: mixed, covariance(unstructured) in Random coefficients. Just like in that section, we could use bayesstats ic after bayesmh to compare the unstructured and independent models.\n\nWe can also use the new mvnexchangeable() prior option to specify an exchangeable random-effects covariance structure instead of an unstructured. An exchangeable covariance is characterized by two parameters, a common variance and a correlation. We specify additional priors for those parameters.", null, "We could fit other models from Bayesian multilevel models using the bayes prefix by using bayesmh. For instance, we could fit the three-level survival model by using\n\n. bayesmh time education njobs prestige i.female U[birthyear] UU[id<birthyear],\nlikelihood(stexponential, failure(failure))\nprior({time:}, normal(0,10000)) prior({var_U var_UU}, igamma(0.01,0.01) split)\n\n\nand the crossed-effects logistic model by using\n\n. bayesmh attain_gt_6 sex U[sid] V[pid], likelihood(logit)\nprior({attain_gt_6:}, normal(0,10000)) prior({var_U var_V}, igamma(0.01,0.01))\n\n\nBut all these models can be easily fit already by the bayes prefix. In what follows, we demonstrate models that cannot be fit with bayes:.\n\n## Nonlinear multilevel models\n\nYou can fit Bayesian univariate nonlinear multilevel models using bayesmh. The bayesmh syntax is the same as the menl command that fits classical nonlinear mixed-effects models, except that bayesmh additionally supports crossed effects such as UV[id1#id2] and latent factors such as L[_n].\n\n## SEM-type models\n\nYou can use bayesmh to fit some structural equation models (SEMs) and models related to them. SEMs analyze multiple variables and use so-called latent variables in their specifications. A latent variable is a pseudo variable that has a different, unobserved, value for each observation. With bayesmh, you specify latent variables as L[_n]. You can use different latent variables in different equations, you can share the same latent variables across equations, you can place constraints on coefficients of latent variables, and more.\n\n## Joint models of longitudinal and survival data\n\nYou can use bayesmh to model multiple outcomes of different types. Joint models of longitudinal and survival outcomes are one such example. These models are popular in practice because of their three main applications:\n\n1. Account for informative dropout in the analysis of longitudinal data.\n\n2. Study effects of baseline covariates on longitudinal and survival outcomes.\n\n3. Study effects of time-dependent covariates on the survival outcome.\n\nBelow, we demonstrate the first application, but the same concept can be applied to the other two.\n\nWe will use a version of the Positive and Negative Symptom Scale (PANSS) data from a clinical trial comparing different drug treatmeans for schizophrenia (Diggle 1998). The data contain PANSS scores (panss) from patients who received three treatments (treat): placebo, haloperidol (reference), and risperidone (novel therapy). PANSS scores are measurements for psychiatric disorder. We would like to study the effects of the treatments on PANSS scores over time (week).\n\nA model considered for PANSS scores is a longitudinal linear model with the effects of treatments, time (in weeks), and their interaction and random intercepts U[id].\n\n. bayesmh panss i.treat##i.week U[id], likelihood(normal({var}))\n\n\nSo how does the survival model come into play here?\n\nMany subjects withdrew from this study—only about half completed the full measurement schedule. Many subjects dropped out because of “inadequate for response”, which suggests that the dropout may be informative and cannot be simply ignored in the analysis.\n\nA dropout process can be viewed as a survival process with an informative dropout (infdrop) as an event of interest and with time to dropout as a survival time. Because we have longitudinal data, there are multiple observations per subject. So the dropout time is split into multiple spells according to week and is thus represented by the beginning time (t0) and end time (t1). At the left time point t0, an observation (or a spell) is considered left-truncated. We will assume a Weibull survival model for the dropout process. The dropout is likely to be related to the treatment, so we include it as the predictor in the survival model.\n\n. bayesmh t1 i.treat, likelihood(stweibull({lnp}) failure(infdrop) ltruncated(t0))\n\n\n\nOne way to account for informative dropout is to include a shared random effect between the longitudinal and survival models that would induce correlation between the longitudinal outcome and the dropout process (Henderson, Diggle, and Dobson 2000).\n\n. bayesmh (panss i.treat##i.week U[id]@1, likelihood(normal({var})))\n(t1 i.treat U[id], likelihood(stweibull({lnp}) failure(infdrop) ltruncated(t0)))\n\n\n\nWe added random intercepts from the longitudinal model to the survival model. We also constrained the coefficient for U[id] in the first equation to 1. We did this to emphasize that only the coefficient for U[id] in the second equation will be estimated. bayesmh actually makes this assumption automatically by default.\n\nTo fit the above model, we need to specify prior distributions for model parameters. We have many parameters, so we may need to specify somewhat informative priors. Recall that Bayesian models, in addition to the main model parameters, also estimate all the random-effects parameters U[id].\n\nIf there is an effect of dropout on the PANSS scores, it would be reasonable to assume that it would be positive. So we specify an exponential prior with scale 1 for the coefficient of U[id] in the survival model. We specify normal priors with mean 0 and variance of 1,000 for the constant {panss:_cons} and Weibull parameter {lnp}. We assume normal priors with mean 0 and variance 100 for other regression coefficients. And we use inverse-gamma priors with shape and scale of 0.01 for the variance components.\n\nTo improve sampling efficiency, we use Gibbs sampling for variance components and perform blocking of other parameters. We also specify initial values for some parameters by using the initial() option.", null, "", null, "We will not focus on the interpretation of all the results from this model, but we will comment on the coefficient {t1:U} for the shared random intercept. It is estimated to be 0.06, and its 95% credible interval does not contain 0. This means there is a positive association between PANSS scores and dropout times: the higher the PANSS score, the higher the chance of dropout. So, simple longitudinal analysis would not be appropriate for these data.\n\n## Multivariate nonlinear growth models\n\nHierarchical linear and nonlinear growth models are popular in many disciplines, such as health science, education, social sciences, engineering, and biology. Multivariate linear and nonlinear growth models are particularly useful in biological sciences to study the growth of wildlife species, where the growth is described by multiple measurements that are often correlated. Such models often have many parameters and are difficult to fit using classical methods. Bayesian estimation provides a viable alternative.\n\nThe above models can be fit by bayesmh using multiple-equation specifications, which now support random effects and latent factors. The equations can be all linear, all nonlinear, or a mixture of the two types. There are various ways to model the dependence between multiple outcomes (equations). For instance, you can include the same random effects but with different coefficients in different equations, or you can include different random effects but correlate them through the prior distribution.\n\nLet’s follow Jones et al. (2005) who applied a Bayesian bivariate growth model to study the growth of black-fronted tern chicks. The growth was measured by wing length y1 and weight y2. A linear growth model is assumed for wing length, and a logistic growth model is assumed for weight.\n\n(y1,ijy2,ij)=(Ui+VitimeijCi/{1+dCiexp(Bitimeij)})+(ε1,ijε2,ij)\n\nwhere d is a fixed parameter, (Ui,Vi,Ci,Bi)N(μ,Σ), and (ε1,ε2)N(0,Σ0).\n\nThere are four random effects at the individual (chick) level: U and V are the intercept and growth rate for the wings. In the equation for y2, we have random effects B and C, which represent the rate and maximum weight. The location parameter is assumed to take the form dC, where d is a constant. (U,V,C,B) follow a multivariate normal distribution with an unstructured covariance. The errors from the two equations follow a bivariate normal distribution.\n\nWe use a fictional dataset simulated based on the description in Jones et al. (2005). We fit a bivariate normal model with error covariance {Sigma0,m}. The four random effects are assigned a multivariate normal prior with the corresponding mean parameters and covariance {Sigma,m}. The prior means are assigned normal distributions with mean 0 and variance 100. The covariance matrices are assigned inverse Wishart priors. Parameter d is assigned an exponential prior with scale 1. We use Gibbs sampling for covariance matrices and block parameters to improve efficiency. We also specify initial values, use a smaller MCMC size of 2,500, and specify a random-number seed for reproducibility.", null, "", null, "Error covariances and random-effects covariance values are not 0, which suggests that the wing length and weight measurements are related.\n\nWe use bayesstats summary to compute correlation estimates.", null, "There is a positive correlation, 0.21, between the error terms.\n\nWe also compute the correlation between the rate of wing growth and the maximum weight.", null, "The estimated correlation is 0.73, which is high. The wing length and weight measurements are clearly correlated and should be modeled jointly." ]

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[ "# Protein and fat deposition in pigs in relation to bodyweight gain and feeding level\n\nW.A.G. Cöp\n\nResearch output: Thesisinternal PhD, WU\n\n## Abstract\n\nIn pig breeding it is quite common to select for bodyweight gain, feed conversion and slaughter quality. Various values have been found by different research- workers for the relationships between these traits. These differences in values have mainly been caused by differences between feeding levels and by those between chemical composition of carcases. Protein and fat deposition can be calculated from bodyweight gain and feed intake; these traits would take into account differences in feeding level and. chemical composition of carcases better than bodyweight gain and feed conversion do.Therefore an investigation was done\n- to find out how precisely protein and fat deposition could be predicted from bodyweight gain, bodyweight and feed intake, and\n- to study the variation in protein and fat deposition at restricted and ad libitum feeding and the relation between these factors, growth and carcase traits.For the calculation of protein and fat deposition three models were obtained from data in the literature (EBC, EBK and MEK models - Section 2.3). These models were based on physiological data connected with bodyweight and feed utilization (maintenance, protein and fat deposition).In the MEK model it was assumed that all ME was used for maintenance, protein and fat deposition according to the following equation:\nME = ME M + c ΔP + d ΔF.The EBC and EBK models started from the energy balance:\nEB = 5.7 ΔP + 9.46 ΔF.In order to estimate the amount of ME P or EB that was used for protein and fat deposition, respectively, the research-workers calculated from literature or their own data the relationships between the components of growth. EB was calculated from ME using the equation\nEB = (ME - ME M ) x efficiency.The equations that were used to calculate protein (ΔP) and fat (ΔF) deposition in the EBC, EM and MEK models, were:\nIn these models 4 factors were varied:\n- maintenance requirement: 80, 100 or 120 kcal ME/kg3/4;\n- efficiency for synthesizing protein and fat from ME P . For the EBC and EBK models the same figure was assumed for protein as for fat: 0. 55, 0.65 or 0. 75. In the MEK model the ME costs (kcal/g) for synthesizing protein and fat were assumed to be: 16 and 13, 13 and 13, or 11.4 and 12.6;\n- the ratio protein to protein + water in the EBC model: a constant value was assumed or a value was calculated from the amount of protein and water at each bodyweight. These amounts have been estimated using allometric equations;\n- the amounts of protein, water and fat gain (in the EBC model) or the amount of bodyweight gain minus gut fill (in the EBK and MEK models). The alternative values of this factor have been obtained using linear or allometric equations between bodyweight and the amounts of ash and gut fill or gut fill.The equations or values used for calculating the values of the 4 factors are shown in Table 3.4.To judge the precision of the prediction of protein and fat deposition the following 4 traits were calculated:\n- the level of protein and fat deposition;\n- the values of correlation coefficients between calculated and found protein and fat deposition.The data used consisted of energy and N balances from 6 different investigations, and results of chemical analysis of the empty body of pigs. In addition, bodyweight gain was estimated using a cubic curve in 3 sets of data mentioned above. Thus, totally 10 sets of data were available for the computations. For the computations the values of correlation coefficients between calculated and found protein and fat deposition were transformed by the Z transformation of FISHER.With the statistical Model 3.1, the following effects were tested for each trait and each model:\n- differences between sets of data,\n- differences between factors, and\n- differences between models.The level of the four traits differed considerably between the various sets of data (Tables 3.5 and 3.7). In addition the interaction between data and factors was always significant. These interactions are also shown in Table 3.6 by the great differences between sets of data for the values of regression coefficients of the traits on the factors. The differences between sets of data might be caused by:\n- differences between feeding level, feed composition, sex or breed;\n- systematic differences between experimental procedures used by the research workers for energy and N balances, weighings etc.Computation of bodyweight gain from a cubic curve doubled the value of the correlation coefficient between calculated and found protein deposition in JUST NIELSEN's data, compared with those, found by using the weight gain obtained from linear interpolation between 2 weighings. Using a cubic curve, in LUDVIGSEN and THORBEK's data the same value of correlation coefficient was found, and in BREIREM's data a lower value, compared with those obtained by calculating bodyweight gain from linear interpolation. The value of the correlation coefficient between calculated and found fat deposition in JUST NIELSEN's data was 0.970, using data from energy balances, compared with 0.257 using chemical analysis of the empty body. With reference to JUST NIELSEN (1970), it has been stated that more data are necessary to be sure about the value and precision of results from energy and N balances or from comparative slaughter techniques.It has been indicated that the interactions between factors and sets of data have been partly caused by systematic differences in the various sets of data between bodyweights of the pigs (Table 3.14).The relative contribution of the variance in calculated protein and fat deposition to differences between sets of data was 60 to 70 % in the three models; the relative contribution to this effect by the variance in the value of correlation coefficients between calculated and found protein and fat deposition was 95 to 99 % (Table 3.8). The relative contribution of the variance in protein and fat deposition to the factors, maintenance and efficiency was - excluding protein deposition in the MEK Model - considerably higher than their contribution to the other two factors.If a higher maintenance requirement, a lower efficiency or a greater amount of water in the bodyweight gain were considered, the protein deposition and the value of the correlation coefficient between calculated and found protein deposition increased; however, then the fat deposition and the value of correlation coefficient between calculated and found fat deposition decreased (Tables 3.6 and 3.15). These changes in protein and fat deposition follow from the equations in Section 2.3, but they can also be explained by the difference between energy content of protein and fat. The changes in the values of correlation coefficients between calculated and found protein and fat deposition has been explained by a non-linear relationship between calculated and found protein and fat deposition.It is doubtful, whether the highest values of the correlation coefficients between calculated and found protein deposition also gave the best prediction of these traits.There were only small differences between the 3 models (Table 3.10). The value of 4.6838 for LBM /protein in the EBK and MEK models was lower than it should be, if based on the average bodyweight of the pigs in the various sets of data. Therefore with this value, protein deposition was overestimated and fat deposition was underestimated. The values of correlation coefficients between calculated and found protein deposition were significantly lower in the MEK model than in the EBC and EBK models.The equations used for the calculation of protein and fat deposition in Chapter 4 were based on the EBK model. To make a choice between the different combinations of the 4 factors it was assumed that:\n- maintenance requirement is 100 kcal ME/kg3/4,\n- protein deposition using N balances was overestimated by 15.5 %, and\nOriginal language English Doctor of Philosophy Politiek, R.D., Promotor, External person 11 Dec 1974 Wageningen Veenman Published - 1974\n\n## Keywords\n\n• pigs\n• weight\n• mass\n• characteristics\n• zoology\n\n## Fingerprint\n\nDive into the research topics of 'Protein and fat deposition in pigs in relation to bodyweight gain and feeding level'. Together they form a unique fingerprint." ]

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[ "# Convergence of \\sqrt{n}x_{n}\\sqrt{n}x_{n} where x_{n+1} = \\sin(x_{n})x_{n+1} = \\sin(x_{n})\n\nConsider the sequence defined as\n\n$x_1 = 1$\n\n$x_{n+1} = \\sin x_n$\n\nI think I was able to show that the sequence $\\sqrt{n} x_{n}$ converges to $\\sqrt{3}$ by a tedious elementary method which I wasn’t too happy about.\n\n(I think I did this by showing that $\\sqrt{\\frac{3}{n+1}} < x_{n} < \\sqrt{\\frac{3}{n}}$, don't remember exactly)\n\nThis looks like it should be a standard problem.\n\nDoes anyone know a simple (and preferably elementary) proof for the fact that the sequence $\\sqrt{n}x_{n}$ converges to $\\sqrt{3}$?\n\nBefore getting into the details, let me say: The ideas I'm talking about, including this exact example, can be found in chapter 8 of Asymptotic Methods in Analysis (second edition), by N. G. de Bruijn. This is a really superb book, and I recommend it to anyone who wants to learn how to approximate quantities in \"calculus-like\" settings. (If you want to do approximation in combinatorial settings, I recommend Chapter 9 of Concrete Mathematics.)\n\nAlso, this isn't just about $\\sin$. Let $f$ be a function with $f(0)=0$ and $0 \\leq f(u) < u$ for $u$ in $(0,c]$ then the sequence $x_n:=f(f(f(\\cdots f(c)\\cdots)$ approaches $0$. If $f(u)=u-a u^{k+1} + O(u^{k+2})$ (with $a>0$) then $x_n \\approx \\alpha n^{-1/k}$ and you can prove that by the same methods here.\n\nHaving said that, the answer to your question. On $[0,1]$, we have\n\nSetting $y_n=1/x_n^2$, we have\n\nso\n\nWe see that\n\nand\n\nSince we already know that $x_n \\to 0$, we know that $y_n^{-1} \\to 0$, so the average goes to zero and we get $\\lim_{n \\to \\infty} y_n/n=1/3$. Transforming back to $\\sqrt{n} x_n$ now follows by the continuity of $1/\\sqrt{t}$." ]

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[ "", null, "Скачать презентацию Singular Value Decomposition in Text Mining Ram Akella\n\n6c27357bb0616e6ee4906e11337540a9.ppt\n\n• Количество слайдов: 34", null, "Singular Value Decomposition in Text Mining Ram Akella University of California Berkeley Silicon Valley Center/SC Lecture 4 b February 9, 2011", null, "Class Outline o o o o Summary of last lecture Indexing Vector Space Models Matrix Decompositions Latent Semantic Analysis Mechanics Example", null, "Summary of previous class o o o Principal Component Analysis Singular Value Decomposition Uses Mechanics Example swap rates", null, "Introduction How can we retrieve information using a search engine? . n We can represent the query and the documents as vectors (vector space model) o However to construct these vectors we should perform a preliminary document preparation. n The documents are retrieved by finding the closest distance between the query and the document vector. o Which is the most suitable distance to retrieve documents?", null, "Search engine", null, "Document File Preparation o Manual Indexing n Relationships and concepts between topics can be established n It is expensive and time consuming n It may not be reproduced if it is destroyed. n The huge amount of information suggest a more automated system", null, "Document File Preparation o. Automatic indexing To buid an automatic index, we need to perform two steps: n Document Analysis Decide what information or parts of the document should be indexed n Token analysis Decide with words should be used in order to obtain the best representation of the semantic content of documents.", null, "Document Normalization After this preliminary analysis we need to perform another preprocessing of the data n Remove stop words o Function words: a, an, as, for, in, of, the… o Other frequent words n Stemming o Group morphological variants n Plurals “ streets” -> “street” n Adverbs “fully” -> “full” o The current algorithms can make some mistakes n “police“, “policy” -> “polic”", null, "File Structures Once we have eliminated the stop words and apply the stemmer to the document we can construct: o. Document File n We can extract the terms that should be used in the index and assign a number to each document.", null, "File Structures o. Dictionary n We will construct a searchable dictionary of terms by arranging them alphabetically and indicating the frequency of each term in the collection Term Global Frequency banana 1 cranb 2 Hanna 2 hunger 1 manna 1 meat 1 potato 1 query 1 rye 2 sourdough 1 spiritual 1 wheat 2", null, "File Structures o. Inverted List n For each term we find the documents and its related position associated with Term (Doc, Position) banana (5, 7) cranb (4, 5); (6, 4) Hanna (1, 7); (8, 2) hunger (9, 4) manna (2, 6) meat (7, 6) potato (4, 3) query (3, 8) rye (3, 3); (6, 3) sourdough (5, 5) spiritual (7, 5) wheat (3, 5); (6, 6)", null, "Vector Space Model n The vector space model can be used to represent terms and documents in a text collection n The document collection of n documents can be represented with a matrix of m X n where the rows represent the terms and the columns the documents n Once we construct the matrix, we can normalize it in order to have unitary vectors", null, "Vector Space Models", null, "Query Matching o If we want to retrieve a document we should: n Transform the query to a vector n look for the most similar document vector to the query. One of the most common similarity methods is the cosine distance between vectors defined as: Where a is the document and q is the query vector", null, "Example: o Using the book titles we want to retrieve books of “Child Proofing” Book titles Query 0 1 0 0 Cos 2=Cos 3=0. 4082 Cos 5=Cos 6=0. 500 With a threshold of 0. 5, the 5 th and the 6 th would be retrieved.", null, "Term weighting o In order to improve the retrieval, we can give to some terms more weight than others. Local Term Weights Where Global Term Weights", null, "Synonymy and Polysemy auto engine bonnet tyres lorry boot car emissions hood make model trunk make hidden Markov model emissions normalize Synonymy Polysemy Will have small cosine Will have large cosine but are related but not truly related", null, "Matrix Decomposition To produce a reduced –rank approximation of the document matrix, first we need to be able to identify the dependence between columns (documents) and rows (terms) n QR Factorization n SVD Decomposition", null, "QR Factorization o The document matrix A can be decomposed as below: Where Q is an m. Xm orthogonal matrix and R is an m. X m upper triangular matrix o This factorization can be used to determine the basis vectors for any matrix A o This factorization can be used to describe the semantic content of the corresponding text collection", null, "Example A=", null, "Example", null, "Query Matching o We can rewrite the cosine distance using this decomposition o Where rj refers to column j of the matrix R", null, "Singular Value Decomposition (SVD) o This decomposition provides a reduced rank approximations in the column and row space of the document matrix o This decomposition is defined as m m m n V is n n Where the columns U are orthogonal eigenvectors of AAT. The columns of V are orthogonal eigenvectors of ATA. Eigenvalues 1 … r of AAT are the square root of the eigenvalues of ATA.", null, "Latent Semantic Decomposition (LSA) o It is the application of SVD in text mining. n We decompose the document-term matrix A into three matrices A V The V matrix refers to terms and U matrix refers to documents U", null, "Latent Semantic Analysis o Once we have decomposed the document matrix A we can reduce its rank n We can account for synonymy and polysemy in the retrieval of documents n Select the vectors associated with the higher value of in each matrix and reconstruct the matrix A", null, "Latent Semantic Analysis", null, "Query Matching o The cosines between the vector q and the n document vectors can be represented as: o where ej is the canonical vector of dimension n This formula can be simplified as where", null, "Example Apply the LSA method to the following technical memo titles c 1: Human machine interface for ABC computer applications c 2: A survey of user opinion of computer system response time c 3: The EPS user interface management system c 4: System and human system engineering testing of EPS c 5: Relation of user perceived response time to error measurement m 1: m 2: m 3: m 4: The generation of random, binary, ordered trees The intersection graph of paths in trees Graph minors IV: Widths of trees and well-quasi-ordering Graph minors: A survey", null, "Example First we construct the document matrix", null, "Example The Resulting decomposition is the following {U} =", null, "Example {S} =", null, "Example {V} =", null, "Example o We will perform a 2 rank reconstruction: n We select the first two vectors in each matrix and set the rest of the matrix to zero n We reconstruct the document matrix", null, "Example The word user seems to have presence in the documents where the word human appears", null, "" ]

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[ "Documentation\n\n# conncomp\n\nConnected graph components\n\n## Syntax\n\n``bins = conncomp(G)``\n``bins = conncomp(G,Name,Value)``\n``[bins,binsizes] = conncomp(___)``\n\n## Description\n\nexample\n\n````bins = conncomp(G)` returns the connected components of graph `G` as bins. The bin numbers indicate which component each node in the graph belongs to.If `G` is an undirected graph, then two nodes belong to the same component if there is a path connecting them.If `G` is a directed graph, then two nodes belong to the same strong component only if there is a path connecting them in both directions.```\n\nexample\n\n````bins = conncomp(G,Name,Value)` uses additional options specified by one or more Name-Value pair arguments. For example, `conncomp(G,'OutputForm','cell')` returns a cell array to describe the connected components.```\n````[bins,binsizes] = conncomp(___)` also returns the size of the connected components. `binsizes(i)` gives the number of nodes in component `i`.```\n\n## Examples\n\ncollapse all\n\nCreate and plot an undirected graph with three connected components. Use `conncomp` to determine which component each node belongs to.\n\n```G = graph([1 1 4],[2 3 5],[1 1 1],6); plot(G)```", null, "`bins = conncomp(G)`\n```bins = 1×6 1 1 1 2 2 3 ```\n\nCreate and plot a directed graph, and then compute the strongly connected components and weakly connected components. Weakly connected components ignore the direction of connecting edges.\n\n```s = [1 2 2 3 3 3 4 5 5 5 8 8]; t = [2 3 4 1 4 5 5 3 6 7 9 10]; G = digraph(s,t); plot(G,'Layout','layered')```", null, "`str_bins = conncomp(G)`\n```str_bins = 1×10 4 4 4 4 4 6 5 1 3 2 ```\n`weak_bins = conncomp(G,'Type','weak')`\n```weak_bins = 1×10 1 1 1 1 1 1 1 2 2 2 ```\n\nUse the second output of `conncomp` to extract the largest component of a graph or to remove components below a certain size.\n\nCreate and plot a directed graph. The graph has one large component, one small component, and several components that contain only a single node.\n\n```s = [1 2 2 3 3 3 4 5 5 5 8 8 9]; t = [2 3 4 1 4 5 5 3 6 7 9 10 10]; G = digraph(s,t,[],20); plot(G,'Layout','layered')```", null, "Calculate the weakly connected components and specify two outputs to `conncomp` to get the size of each component.\n\n`[bin,binsize] = conncomp(G,'Type','weak')`\n```bin = 1×20 1 1 1 1 1 1 1 2 2 2 3 4 5 6 7 8 9 10 11 12 ```\n```binsize = 1×12 7 3 1 1 1 1 1 1 1 1 1 1 ```\n\nUse `binsize` to extract the largest component from the graph. `idx` is a logical index indicating whether each node belongs to the largest component. The `subgraph` function extracts the nodes selected by `idx` from `G`.\n\n```idx = binsize(bin) == max(binsize); SG = subgraph(G, idx); plot(SG)```", null, "A similar use of `binsizes` is to filter out components based on size. The procedure is similar to extracting the largest component, however in this case each node can belong to any component that meets the size requirement.\n\nFilter out any components in `G` that have fewer than 3 nodes. `idx` is a logical index indicating whether each node belongs to a component with 3 or more nodes.\n\n```idx = binsize(bin) >= 3; SG = subgraph(G, idx); plot(SG)```", null, "## Input Arguments\n\ncollapse all\n\nInput graph, specified as either a `graph` or `digraph` object. Use `graph` to create an undirected graph or `digraph` to create a directed graph.\n\nExample: `G = graph(1,2)`\n\nExample: `G = digraph([1 2],[2 3])`\n\n### Name-Value Pair Arguments\n\nSpecify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.\n\nExample: `bins = conncomp(G,'OutputForm','cell')`\n\nType of output, specified as the comma-separated pair consisting of `'OutputForm'` and either `'vector'` or `'cell'`.\n\nOptionOutput\n`'vector'` (default)`bins` is a numeric vector indicating which connected component each node belongs to.\n`'cell'``bins` is a cell array, and `bins{j}` contains the node IDs for all nodes that belong to component `j`.\n\n### Note\n\nThe `'Type'` option is supported only for directed graphs created using `digraph`.\n\nType of connected components, specified as the comma-separated pair consisting of `'Type'` and either `'strong'` (default) or `'weak'`.\n\nOptionResult\n`'strong'` (default)Two nodes belong to the same connected component only if there is a path connecting them in both directions.\n`'weak'`Two nodes belong to the same connected component if there is a path connecting them, ignoring edge directions.\n\nExample: `bins = conncomp(G,'Type','weak')` computes the weakly connected components of directed graph `G`.\n\n## Output Arguments\n\ncollapse all\n\nConnected components, returned as a vector or cell array. The bin numbers assign each node in the graph to a connected component:\n\n• If `OutputForm` is `'vector'` (default), then `bins` is a numeric vector indicating which connected component (bin) each node belongs to.\n\n• If `OutputForm` is `'cell'`, then `bins` is a cell array, with `bins{j}` containing the node IDs for all nodes that belong to component `j`.\n\nSize of each connected component, returned as a vector. `binsizes(i)` gives the number of elements in component `i`. The length of `binsizes` is equal to the number of connected components, `max(bins)`.\n\ncollapse all\n\n### Weakly Connected Components\n\nTwo nodes belong to the same weakly connected component if there is a path connecting them (ignoring edge direction). There are no edges between two weakly connected components.\n\nThe concepts of strong and weak components apply only to directed graphs, as they are equivalent for undirected graphs.\n\n### Strongly Connected Components\n\nTwo nodes belong to the same strongly connected component if there are paths connecting them in both directions. There can be edges between two strongly connected components, but these connecting edges are never part of a cycle.\n\nThe bin numbers of strongly connected components are such that any edge connecting two components points from the component of smaller bin number to the component with a larger bin number.\n\nThe concepts of strong and weak components apply only to directed graphs, as they are equivalent for undirected graphs." ]

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[ "Python actual combat (IV) | number\nfeiren_ java 2021-07-25 10:35:51\n01 Preface\n\nMy brother is a dog , A programmer . done Android、 Rolled over Java、 At present, I am studying myself Python . register 「 A good loser 」 This company has been for some days , The idea that really wants to operate it is the idea that came into being in these two days . The original intention of registering this number is to share my Python Learning notes . A knowledge , You know , Not really understand , You can make others understand , Is to really master . Share , It's the best review process .\n\n02 What is? Python Numbers (Number)\n\nPython The numeric data type is used to store values .\nData type cannot be changed , This means that if you change the value of a numeric data type , Memory space will be reallocated .\nThe following example is used in variable assignment Number Object will be created ：\n\n```var1 = 1\nvar2 = 10\n```\n\nYou can also use the del Statement to delete references to some numeric objects .\ndel The syntax of the sentence is ：\n\n```del var1[,var2[,var3[....,varN]]]]\n```\n\nYou can use the del Statement to delete references to single or multiple objects , for example ：\n\n```del var\ndel var_a, var_b\n```\n\nPython Three different numerical types are supported ：\n\n• integer (Int) - It's usually called an integer or an integer , It's a positive or negative integer , Without decimal point .Python3 There is no limit to the size of an integer , Can be viewed as Long Type used , therefore Python3 No, Python2 Of Long type .\n• floating-point (float) - Floating point type consists of integer part and decimal part , Floating point types can also be represented by scientific notation （2.5e2 = 2.5 x 102 = 250）\n• The plural ( (complex)) - The plural consists of the real part and the imaginary part , It can be used a + bj , perhaps complex(a,b) Express , The real part of a complex number a Deficiency part of harmony b It's all floating point .\n\nWe can use hexadecimal and octal to represent integers ：\n\n```>>> number = 0xA0F # Hexadecimal\n>>> number\n2575\n>>> number=0o37 # octal\n>>> number\n31\n```\nint float complex\n10 0.0 3.14j\n100 15.20 45.j\n-786 -21.9 9.322e-36j\n080 32.3+e18 .876j\n-0490 -90. -.6545+0J\n-0x260 -32.54e100 3e+26J\n0x69 70.2-E12 4.53e-7j\n\nPython Support complex number , The plural consists of the real part and the imaginary part , It can be used a + bj, perhaps complex(a,b) Express , The real part of a complex number a Deficiency part of harmony b It's all floating point .\n\n#### Python Digital type conversion\n\noccasionally , We need to transform the built-in types of data , Conversion of data types , You just need to use the target data type you want to convert as the function name .\n\ngrammar ： Target data type ( Variable )\n\n• int(x) take x Convert to an integer .\n\n• float(x) take x Converts to a floating point number .\n\n• complex(x) take x To a complex number , The real part is x, The imaginary part is 0.\n\ncomplex(x, y) take x and y To a complex number , The real part is x, The imaginary part is y.x and y It's a number expression .\nThe following example shows floating point variables a Convert to integer ：\n\n```>>> a = 1.0\n>>> int(a)\n1\n```\n03 Python Number operation\n\nPython The interpreter can be used as a simple calculator , You can enter an expression in the interpreter , It will output the value of the expression .\nThe syntax of expressions is straightforward ： +, -, ***** and /, And other languages （ Such as Java or C） Same as in . for example ：\n\n```>>> 2 + 2\n4\n>>> 50 - 5*6\n20\n>>> (50 - 5*6) / 4\n5.0\n>>> 8 / 5 # Always return a floating point number\n1.6\n```\n\nBe careful ： The result of floating-point operation may be different on different machines .\n\nIn integer division , division / Always return a floating point number , If you just want to get the result of integers , Discard possible fractions , You can use operators // ：\n\n```>>> 17 / 3 # Integer division returns floating point\n5.666666666666667\n>>>\n>>> 17 // 3 # Integer division returns the result of rounding down\n5\n>>> 17 % 3 # ％ The operator returns the remainder of the division\n2\n>>> 5 * 3 + 2\n17\n```\n\nBe careful ：// What you get is not necessarily a number of integer type , It has something to do with the data type of denominator .\n\n```>>> 7//2\n3\n>>> 7.0//2\n3.0\n>>> 7//2.0\n3.0\n```\n\nEqual sign = Used to assign values to variables . After the assignment , Except for the next prompt , The interpreter doesn't show any results .\n\n```>>> width = 20\n>>> height = 5*9\n>>> width * height\n900\n```\n\nPython have access to \"\"** Operation to do the power operation ：\n\n```>>> 5 ** 2 # 5 The square of\n25\n>>> 2 ** 7 # 2 Of 7 Power\n128\n```\n\nVariables must be changed before they are used \" Definition \"（ That is to give a value to the variable ）, Otherwise, an error will occur ：\n\n```>>> n # Trying to access an undefined variable\nTraceback (most recent call last):\nFile \"<stdin>\", line 1, in <module>\nNameError: name 'n' is not defined\n```\n\nDifferent types of mixed operations convert integers to floating-point numbers ：\n\n```>>> 3 * 3.75 / 1.5\n7.5\n>>> 7.0 / 2\n3.5\n```\n\nIn interactive mode , Finally, the output expression result is assigned to the variable _ . for example ：\n\n```>>> tax = 12.5 / 100\n>>> price = 100.50\n>>> price * tax\n12.5625\n>>> price + _\n113.0625\n>>> round(_, 2)\n113.06\n```\n\nhere , _ Variables should be treated by the user as read-only variables .\n\n04 Mathematical functions\n\nPython Contains the following common mathematical functions ：\n\nfunction Return value ( describe )\nabs(x) Returns the absolute value of the number , Such as abs(-10) return 10\nceil(x) Returns an upinteger of a number , Such as math.ceil(4.1) return 5\ncmp(x, y) If x < y return -1, If x == y return 0, If x > y return 1. Python 3 obsolete . Use Use (x>y)-(x<y) Replace .\nexp(x) return e Of x The next power (ex), Such as math.exp(1) return 2.718281828459045\nfabs(x) Returns the absolute value of the number , Such as math.fabs(-10) return 10.0\nfloor(x) Returns the rounded value of a number , Such as math.floor(4.9) return 4\nlog(x) Such as math.log(math.e) return 1.0,math.log(100,10) return 2.0\nlog10(x) Return to 10 For the base x The logarithmic , Such as math.log10(100) return 2.0\nmax(x1, x2,...) Returns the maximum value of the given parameter , Parameters can be sequences .\nmin(x1, x2,...) Returns the minimum value for a given parameter , Parameters can be sequences .\nmodf(x) return x The integral and fractional parts of , Two parts of the numerical symbols and x identical , The integer part is represented as a floating point .\npow(x, y) x**y The calculated value .\nround(x [,n]) Return floating point number x Round the value of , Such as given n value , Represents the number rounded to the decimal point .\n05 Random number function\n\nRandom numbers can be used in Mathematics , game , In areas such as security , It's often embedded in algorithms , To improve the efficiency of the algorithm , And improve the security of the program .\nPython Contains the following common random number functions ：\n\nfunction describe\nchoice(seq) Pick one element at random from the elements of the sequence , such as random.choice(range(10)), from 0 To 9 Pick an integer at random .\nrandrange ([start,] stop [,step]) From the specified range , Gets a random number from a set incremented by the specified cardinality , The cardinality default is 1\nrandom() I'm going to randomly generate the next real number , It's in [0,1) Within the scope of .\nseed([x]) Change the seed of the random number generator seed. If you don't know how it works , You don't have to specify seed,Python Will help you choose seed.\nshuffle(lst) Sort all the elements of the sequence at random\nuniform(x, y) I'm going to randomly generate the next real number , It's in [x,y] Within the scope of .\n06 Trigonometric functions\n\nPython Include the following trigonometric functions ：\n\nfunction describe\nacos(x) return x Of arc cosine radians .\nasin(x) return x Of arc sine radians .\natan(x) return x The arctangent of PI radians .\natan2(y, x) Returns the given X And Y The inverse tangent of the coordinate value .\ncos(x) return x Cosine of PI radians .\nhypot(x, y) Returns the Euclidean norm sqrt(xx + yy).\nsin(x) Back to x Sine of radians .\ntan(x) return x Tangent of radians .\ndegrees(x) Convert radians to degrees , Such as degrees(math.pi/2) , return 90.0\n07 Mathematical constant\nConstant describe\npi Mathematical constant pi（ PI , General with π To express ）\ne Mathematical constant e,e That is the constant of nature （ constants ）.\n08 Afterword\n\nOkay , The article is over , Don't be surprised if you see similar articles elsewhere , It's just that someone is jealous of my talent , Let them go . Don't talk much , I have specially arranged a mind map for you so that you can understand and remember the knowledge of this chapter .", null, "That's all for this section , Next section ： self-taught Python The string of (String)\n\nSimilar articles\n\n2021-06-04\n\n2021-06-04\n\n2021-06-04\n\n2021-06-05\n\n2021-06-05\n\n2021-06-05\n\n2021-06-06\n\n2021-06-06\n\n2021-06-07\n\n2021-06-07\n\n2021-06-09\n\n2021-06-09\n\n2021-06-09\n\n2021-06-09\n\n2021-06-09\n\n2021-06-09\n\n2021-06-10\n\n2021-06-11\n\n2021-06-12\n\n2021-06-12\n\n2021-06-16\n\n2021-07-24\n\n2021-07-25\n\n2021-07-28\n\n2021-07-30\n\n2021-08-02\n\n2021-08-04\n\n2021-08-05" ]

[ null, "https://inotgo.com/imagesLocal/202106/30/20210630174309428y_0.png.jpg", null ]

[ "# Examples On Tangents To Ellipses Set-4\n\nGo back to  'Ellipse'\n\nExample - 22\n\nProve that in any ellipse, the perpendicular from a focus upon any tangent and the line joining the centre of the ellipse to point of contact meet on the corresponding directrix.\n\nSolution: Let the ellipse be \\begin{align}\\frac{{{x^2}}}{{{a^2}}} + \\frac{{{y^2}}}{{{b^2}}} = 1\\end{align}  and let a tangent be drawn to it at an arbitrary point $$P(a\\cos \\theta ,\\,b\\sin \\theta )$$ as shown :", null, "We need to show that the perpendicular from F onto this tangent, i.e., FT, and the line joining the centre to the point of contact, i.e. OP intersect on the corresponding directrix; in other words, we need to show that the x-coordinate of Q as in the figure above is \\begin{align}x = \\frac{a}{e}.\\end{align}\n\nThe equation of the tangent at P is $$\\frac{x}{a}\\cos \\theta + \\frac{y}{b}\\sin \\theta = 1.$$\n\nThe slope of this tangent is $${m_T} = \\frac{{ - b}}{a}\\cot \\theta$$\n\nTherefore, the slope of FT is\n\n${m_{FT}} = \\frac{a}{b}\\tan \\theta$\n\nThe equation of FT is\n\n$FT: y = \\left( {\\frac{a}{b}\\tan \\theta } \\right)(x - ae)\\quad\\quad\\quad...\\left( 1 \\right)$\n\nThe equation of OP is simply\n\n$OP:y = \\left( {\\frac{b}{a}\\tan \\theta } \\right)x \\quad\\quad\\quad...\\left( 2 \\right)$\n\nComparing (1) and (2) gives $$x = a/e,$$ which proves the stated assertion.\n\nExample - 23\n\nFind the coordinates of all the points on the ellipse \\begin{align}\\frac{{{x^2}}}{{{a^2}}} + \\frac{{{y^2}}}{{{b^2}}} = 1\\end{align} for which the area of $$\\Delta PON$$ is the maximum where O is the origin and N is the foot of the perpendicular from O to the tangent at P.\n\nSolution: We can assume the point P to be $$(a\\cos \\theta ,\\,b\\sin \\theta )$$ so that the tangent at P has the equation\n\n$\\frac{x}{a}\\cos \\theta + \\frac{y}{b}\\sin \\theta = 1\\quad\\quad\\quad...\\left( 1 \\right)$", null, "To evaluate the area of $$\\Delta PON,$$ we first need the coordinates of the point N. The equation of ON is\n\n\\begin{align}&y - 0 = \\frac{a}{b}\\tan \\theta (x - 0)\\\\ &\\Rightarrow\\quad ax\\sin \\theta - by\\cos \\theta = 0\\qquad\\qquad...\\left( 2 \\right)\\end{align}\n\nThe intersection of (1) and (2) gives us the coordinates of N as\n\n$N \\equiv \\left( {\\frac{{a{b^2}\\cos \\theta }}{{{a^2}{{\\sin }^2}\\theta + {b^2}{{\\cos }^2}\\theta }},\\,\\frac{{{a^2}b\\sin \\theta }}{{{a^2}{{\\sin }^2}\\theta + {b^2}{{\\cos }^2}\\theta }}} \\right)$\n\nThe length PN can now be evaluated using the distance formula :\n\n$PN = \\frac{{({a^2} - {b^2})\\sin \\theta \\cos \\theta }}{{\\sqrt {{a^2}{{\\sin }^2}\\theta + {b^2}{{\\cos }^2}\\theta } }}$\n\nThe length ON is simply the perpendicular distance of O from the tangent at P given by (1) :\n\n$ON = \\frac{{ab}}{{\\sqrt {{a^2}{{\\sin }^2}\\theta + {b^2}{{\\cos }^2}\\theta } }}$\n\nThus, the area of $$\\Delta OPN$$ is\n\n\\begin{align}&\\Delta = \\frac{1}{2} \\times PN \\times ON\\\\&\\quad{\\rm{ }} = \\frac{{ab({a^2} - {b^2})}}{2}\\frac{{\\sin \\theta \\cos \\theta }}{{{a^2}{{\\sin }^2}\\theta + {b^2}{{\\cos }^2}\\theta }}\\\\&\\quad{\\rm{ }} = \\frac{{{a^2} - {b^2}}}{2}\\frac{1}{{\\frac{a}{b}\\tan \\theta + \\frac{b}{a}\\cot \\theta }}\\end{align}\n\nThe expression $$\\frac{a}{b}\\tan \\theta + \\frac{b}{a}\\cot \\theta$$ is of the form $$y + \\frac{1}{y}$$ whose minimum magnitude is 2, when\n\n\\begin{align}&\\frac{a}{b}\\tan \\theta = \\pm 1\\\\ &\\Rightarrow \\quad\\tan \\theta = \\pm \\frac{b}{a}\\\\ & \\Rightarrow\\quad \\sin \\theta = \\pm \\frac{b}{{\\sqrt {{a^2} + {b^2}} }},\\,\\cos \\theta = \\pm \\frac{a}{{\\sqrt {{a^2} + {b^2}} }}\\end{align}\n\nWhen this minimum is achieved, $$\\Delta$$ is maximum. Thus, the possible coordinates of P for which area $$(\\Delta OPN)$$ is maximum are\n\n$P \\equiv \\left( { \\pm \\frac{{{a^2}}}{{\\sqrt {{a^2} + {b^2}} }},\\,\\, \\pm \\frac{{{b^2}}}{{\\sqrt {{a^2} + {b^2}} }}} \\right)$\n\nAs might have been expected from symmetry, there are four such possible points on the ellipse.\n\nEllipses\ngrade 11 | Questions Set 1\nEllipses\nEllipses\ngrade 11 | Questions Set 2\nEllipses" ]

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[ "# Separable neural signatures of confidence during perceptual decisions\n\n1. Laboratoire des Systèmes Perceptifs (CNRS UMR 8248), DEC, ENS, PSL University, France\n2. Laboratoire de Neurosciences Cognitives et Computationnelles (Inserm U960), DEC, ENS, PSL University, France\n13 figures, 2 tables and 1 additional file\n\n## Figures\n\nFigure 1", null, "Procedure. (a) Stimulus presentation: stimuli were presented at an average rate of 3 Hz, but with variable onset and offset (vs∈83,133 ms, vss+ves-1≥216 ms; see Materials and methods). Stimuli were presented within a circular annulus which acted as a colour guide for the category distributions. The colour guide and the fixation point were present throughout the trial. (b) Free task: on each trial observers were presented with a sequence of oriented Gabors, which continued until the observer entered their response (or 40 samples were shown). 100 sequences were predefined and repeated three times. (c) Replay task: The observer was presented with a specific number of samples and could only enter their response after the cue (fixation changing to red). The number of samples (x) was determined relative to the number the observer chose to respond to on that same sequence in the Free task (p). There were three intermixed conditions, Less (x = pmin – 2; where pmin is the minimum p of the three repeats), Same (x = pmed; where pmed is the median p) and More (x = pmax + 4; where pmax is the maximum p of the three repeats of that predefined sequence). (d) Categories were defined by circular Gaussian distributions over the orientations, with means -45° (ψ1, blue) and 45° (ψ2, orange), and concentration κ=0.5. The distributions overlapped such that an orientation of 45° was most likely drawn from the orange distribution but could also be drawn from the blue distribution with lower likelihood. (e) The optimal observer accumulates the difference in the evidence for each category, which is defined as the log probability of the sample orientation (θ) given the distributions. The perceptual decision is determined by the sign of the accumulated evidence, where the evidence accumulated across more samples better differentiates the true categories (example evidence traces are coloured by the true category).\nFigure 2", null, "Behaviour and computational modelling. (a) Proportion correct in each condition of the Replay task, relative to the Free task (orange horizontal lines). Individual data are shown in scattered points, error bars show 95% between- (thin) and 95% within- (thick) subject confidence intervals. Open red markers show the model prediction. (b) Distributions of the number of samples per trial in the Free task, and Replay task conditions (over all observers). (c) Difference in log-likelihood of the models utilising a covert bound relative to the models with no covert bound. On the left, the model fitting perceptual decisions only. The middle bar shows the difference in log-likelihood of the fit to confidence ratings with identical perceptual and confidence bounds. The right bar shows the difference in log-likelihood of the fit to confidence ratings of the model with an independent bound for confidence evidence accumulation. Error bars show 95% between-subject confidence intervals. (d) The computational architecture of perceptual and confidence decisions, based on model comparison. Perceptual and confidence decisions accumulate the same noisy perceptual evidence, but confidence is affected by additional noise (εc) and a separate temporal bias (αc). This partial dissociation allows confidence evidence accumulation to continue after the observer has committed to a perceptual decision. (e) Predicted proportion correct compared to actual proportion correct for each observer, based on the fitted model parameters of the final computational model. The left panel shows proportion correct split by condition, and the right, split by confidence rating. (f) Regression coefficients from the GLM analysis showing the relationship between the optimal evidence L, and observers’ perceptual (top) and confidence (bottom) responses for trials split by condition. The right set of bars show the same analysis but with evidence accumulated up to four samples from the response cue.\nFigure 3", null, "EEG signatures of premature perceptual decisions. (a). Classifier AUC training at each time-point in the Free task and testing across time in the Less (top), Same (middle), and More (bottom) conditions of the Replay task. Black contours encircle regions where the mean is 3.1 standard deviations from chance (0.5; 99% confidence). (b) Difference in AUC between the More and Less conditions. Cluster corrected significant differences are highlighted. (c) The relationship between the evidence accumulated up to n samples prior to the response cue and the strength of the neural signature of response execution in each condition. Error bars show 95% within- (thick) and between-subject (thin) confidence intervals.\nFigure 4", null, "Representation of decision variables. (a) Representation precision (Fischer transformed correlation coefficient, z) of stimulus orientation (blue, left), momentary decision update (green, middle), and accumulated decision evidence (purple, right). The encoded variables are shown in the insets (the accumulated evidence is the cumulative sum of the momentary evidence signed by the response, only one example sequence is shown). Shaded regions show 95% between-subject confidence intervals. (b) Relative electrode representation precision over three characteristic time windows (100–200 ms, left; 400–600 ms, middle; and 600–800 ms, right). (c) Representation precision for epochs leading to optimal and suboptimal perceptual (T1) and confidence (T2) responses. Lighter lines show perceptual decisions that match the optimal response, dashed lines show suboptimal confidence ratings. Dashed red horizontal lines show significant interactions between perceptual and confidence suboptimality. The light red horizontal line shows the significant effect of suboptimal perception and the dark red horizontal line shows the significant effect of suboptimal confidence. Shaded regions show 95% within-subject confidence intervals. (d) Difference in decoding precision between the More and the Less conditions for epochs corresponding to the last four samples of the trial. The purple horizontal line shows the significant difference in decoding of accumulated evidence.\nFigure 5", null, "Clusters of behaviourally relevant representations and their sources. (a) Log likelihood ratio (LLR) of the data given the hypothesis that decoding precision varies with behavioural suboptimalities, against the null hypothesis that decoding precision varies only with measurement noise. Perceptual (Type-I) behaviour is shown on top and confidence (Type-II) behaviour is shown on the bottom. Clusters where the log posterior odds ratio outweighed the prior are circled, only the bold area of the perceptual cluster was further analysed. Time series (left) show the maximum LLR of electrodes laterally, with frontal polar electrodes at the top descending to occipital electrodes at the bottom. Scalp maps (right) show the summed LLR over the indicated time windows. (b) Left: representation precision (z) training and testing on signals within the clusters. Colours correspond to the circles in (a), with the dark green bar showing the combined decoding precision of the anterior and posterior confidence clusters, and the black bar showing the combined representation precision of all clusters. Right: Representation precision of the last four samples in the Less and the More conditions for the combined confidence representation and the perceptual representation. Error bars show 95% within-subject confidence intervals. (c) ROIs (defined by mindBoggle coordinates; Klein et al., 2017): lateral occipital cortex (blue); superior parietal cortex (green); orbitofrontal cortex (orange); and rostral middle frontal cortex (red). (d) ROI time series for Noise Max (black) and Noise Min (coloured) epochs, taking the average rectified normalised current density (z) across participants. Shaded regions show 95% within-subject confidence intervals, red horizontal lines indicate cluster corrected significant differences. Standardised within-subject differences are traced above the x-axis, with the shaded region marking z = 0 to z = 1.96 (95% confidence). (e) Standardised regression weight (t-statistic) of the GLM comparing observers’ confidence ratings to those predicted from the activity localised to the orbitofrontal cortex. The shaded region shows the 95% between-subject confidence interval, and the red horizontal line marks the time-window showing cluster-corrected significant differences from 0.\nAppendix 1—figure 1", null, "Schematic of possible relationships between perceptual (Type-I) and confidence (Type-II) evidence accumulation. (a) Same evidence accumulation processes: Type-I (perceptual) and Type-II (confidence) decisions are different responses to the same evidence: each sample of perceptual evidence is disrupted by a sample of sensory noise (εs) drawn from a zero-mean Gaussian with standard deviation σ, and accumulated with a temporal bias described by αs. (b) Parallel processing: Type-I and Type-II decisions rely on entirely separate processing of the same physical stimulus: the confidence decision also incurs noise and temporal integration bias (with subscript c), but these may vary independently of the perceptual processing suboptimalities (subscript s). (c) Partial dissociation: Type-I and Type-II decisions rely on partially dissociable accumulation of the same evidence.\nAppendix 2—figure 1", null, "Model simulation of accumulated evidence for perceptual and confidence decisions. (a) Example trial from one observer showing simulated evidence traces agreeing with the observer’s response (blue) and a sample of example traces which did not agree (red). The perceptual decision is shown on the left. An evidence trace was taken to agree with the observer’s decision if the corresponding bound was reached prior to the opposing bound, or if no bound was reached but the final accumulated evidence was in favour of the chosen option. The median evidence trace (thick blue line) was calculated assuming the evidence that reached the bound early was maintained until the response was entered. For the confidence rating (right) we compared the median evidence from traces where the final accumulator (plus one additional sample of noise) agreed with the observer’s confidence rating. We examined the difference from the ideal accumulated evidence (thick green line) relative to the likelihood of the observers’ rating given all simulated evidence traces. (b) Median final simulated accumulated evidence for the perceptual decision (abscissa), and the confidence decision (ordinate) for all trials of the example observer, colours indicate the condition. (c) Correlation (Fisher transformed z) between perceptual and confidence evidence for each observer. The example observer is highlighted in orange.\nAppendix 3—figure 1", null, "Confidence behaviour. (a) proportion correct (in the perceptual decision) by confidence rating. (b) Decision evidence (based on the presented samples) by confidence rating. (c) Number of samples presented by confidence rating. In all plots, error bars show 95% within-subject confidence intervals. Red circles show the predictions of the best fitting confidence model (Appendix 1). (d) Confidence responses of two observers (top and bottom panels) on all trials sorted by the confidence evidence of the optimal observer. The median confidence evidence (shown by a black vertical line) defines an optimal confidence observer whose confidence above this median are rated high. Observers’ high confidence ratings are shown in blue and low confidence ratings in green. Suboptimal confidence ratings, where human and optimal confidence observers do not match, are indicated with small vertical segments (green for Type-II misses and blue for Type-II false alarms). Negative confidence evidence corresponds to incorrect perceptual decisions. The observer shown on top clearly has fewer suboptimal responses compared with the observer below, and the frequency of suboptimal responses decreases further from the median. (e) Model estimated confidence error by confidence rating suboptimality (0 = the observer’s confidence rating was the same as the optimal observer, 1 = suboptimal confidence rating). (f) The effect of response bias on the analysis of suboptimal confidence in the EEG representation of accumulated evidence. Observers’ confidence ratings were compared to an unbiased optimal observer (purple), and two biased (but otherwise optimal) observers, who respond with high confidence on 35% and 65% of trials (making the human observers relatively more liberal and conservative with their response strategy in comparison). Thick lines show the within-subject difference in precision (Fisher transformed correlation) between trials where the human observers’ confidence ratings correspond to the (un/biased) optimal observer and suboptimal confidence ratings. Shaded regions show the 95% between-subject confidence intervals on the difference.\nAppendix 4—figure 1", null, "Amplitude modulations with task variables. (a) The Laterised readiness potential by condition (top), perceptual decision accuracy (middle) and reported confidence (bottom). Horizontal red lines mark significant differences in amplitude. (b) Central Parietal Positivity, with the same comparisons. Shaded regions show 95% within subject confidence intervals, and the region of slope comparison for the CPP is highlighted in grey.\nAppendix 5—figure 1", null, "Response Classification analysis. (a) Classifier AUC training and testing at each time point (abscissa) based on the power (dB) in each frequency band (ordinate). Clusters where average performance is greater than 3.1 standard deviations (99% confidence) from baseline (0.5) are circled in black. (b) Scalp map of the difference in power for right- compared to left-handed responses averaged over 8 to 32 Hz and −0.5 to 05 s around the response. (c) Classifier performance (AUC) training and testing at each time point, in each condition of the Replay task and in the Free task.\nAppendix 6—figure 1", null, "Encoding variable regression. (a) Encoded variables used to regress EEG signals. The encoded orientation (Cθ, left) and encoded momentary decision update (Cl, middle) were dependent on the orientation presented to the observer. The encoded accumulated evidence (Cz) varied over all presented orientations in a trial, the figure on the right shows only one example. (b) Representation precision of encoding variables using different low-pass filters. (c) Cross correlation between encoding variables over consecutive samples. (d) Temporal generalisation of representations: the regression weights were calculated on EEG signals at each time point and precision was tested across time. Colour scales are relative to the maximal precision, with zero precision in white and negative in grey (a sign flip of the regression weights). (e) Representation precision of the accumulated evidence for the first (left) and last (right) four stimuli of the Less and More conditions. Shaded error bars show the 95% within subject confidence intervals, red horizontal bars mark cluster corrected significant differences between conditions. (f) Representation precision of the previous (n-1), current (n) and future (n+1) accumulated evidence, based on the EEG signals locked to the current epoch. (g) Representation precision of the momentary decision update (top) and the accumulated evidence (bottom) for epochs separated by the timing of the subsequent stimulus, shown in coloured bars (317 ms, red, left; 333 ms, green, middle; and 350 ms blue, right).\nAppendix 8—figure 1", null, "Estimating inference error. (a) Two approaches to estimate inference error. It is assumed the observer’s behaviour is based on a suboptimal inference over the physical stimulus. We do not have access to the single-sample inference error, but can estimate it using the measured variables: the physical stimulus properties, the behaviour, and the EEG signals. Two approaches are outlined: The EEG inference error estimate, which relies on the error of the representation of the accumulated evidence, in clusters where the precision of the representation is related to suboptimal behaviour; and the model error, which relies on simulating the processing of the evidence based on the fitted model parameters, and taking the median of simulated traces which concur with the observer’s response. (b) Correlation between variables measured from behaviour, the stimulus input, and the estimated inference error. (c) Effect size on the difference between Noise Min and Noise Max epochs.\nAppendix 9—figure 1", null, "Regions of interest and corresponding current density. (a) Average rectified normalised current density in Noise Min epochs for the corresponding time windows, filtered above the half-maximum amplitude (b) Regions of interest based on Mindboggle coordinates. (c) Average normalised rectified current density in the right (top) and left (bottom) hemispheres. Noise Min epochs are shown coloured, Noise Max in black, with shaded regions showing the 95% within-subject confidence interval.\n\n## Tables\n\nAppendix 1—table 1\nAppendix 1—table 2\n\n###### Transparent reporting form\nhttps://cdn.elifesciences.org/articles/68491/elife-68491-transrepform-v1.pdf\n\nA two-part list of links to download the article, or parts of the article, in various formats." ]

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[ "# How to find B^(-1)?;We know that B^2=B+2I_3\n\n##", null, "Apr 2, 2017\n\n${B}^{- 1} = \\left(\\frac{1}{2}\\right) B - \\left(\\frac{1}{2}\\right) {I}_{3}$.\n\n#### Explanation:\n\nYou have\n\n${B}^{2} = B + 2 {I}_{3}$.\n\nMultiply by ${B}^{- 1}$:\n\n$B = {I}_{3} + 2 B$^{-1}#\n\nAnd then from simple algebra:\n\n$\\left(\\frac{1}{2}\\right) B - \\left(\\frac{1}{2}\\right) {I}_{3} = {B}^{- 1}$.\n\nApr 2, 2017\n\n${B}^{-} 1 = \\frac{1}{2} \\left(B - {I}_{3}\\right)$\n\n#### Explanation:\n\nAny matrix $B$ obeys it's characteristic polynomial\n\nGiven $B = \\left(\\begin{matrix}0 & 1 & 1 \\\\ 1 & 0 & 1 \\\\ 1 & 1 & 0\\end{matrix}\\right)$ we have\n\n${B}^{3} - 3 B - 2 {I}_{3} = {0}_{3}$ because\n\n$p \\left(\\lambda\\right) = {\\lambda}^{3} - 3 \\lambda - 2$\n\nNow multiplying by left this relationship we have\n\n${B}^{-} 1 {B}^{3} - 3 {B}^{-} 1 B - 2 {B}^{-} 1 = {0}_{3}$ or\n\n${B}^{2} - 3 {I}_{3} - 2 {B}^{-} 1 = {0}_{3}$ then\n\n$2 {B}^{-} 1 = {B}^{2} - 3 {I}_{3}$ but\n\n${B}^{2} = B + 2 {I}_{3}$ so finally\n\n${B}^{-} 1 = \\frac{1}{2} \\left(B - {I}_{3}\\right)$" ]

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[ "Contents\n\n# Contents\n\n## Idea\n\nIn computer science, a monad describes a “notion of computation”. Formally, it is a map that\n\n• sends every type $X$ of some given programming language to a new type $T(X)$ (called the “type of $T$-computations with values in $X$”);\n\n• is equipped with a rule for composing two functions of the form $f : X \\to T(Y)$ (called Kleisli functions) and $g : Y \\to T(Z)$ to a function $g \\circ f : X \\to T (Z)$ (their Kleisli composition);\n\n• is in a way that is associative in the evident sense and unital with respect to a given unit function called $pure_X : X \\to T(X)$, to be thought of as taking a value to the pure computation that simply returns that value.\n\nThis is essentially the same structure as a monad in category theory, but presented differently; see below for the precise relationship.\n\n### For imperative programs in functional programming\n\nMonads provide one way to “embed imperative programming in functional programming”, and are used that way notably in the programming language Haskell. But monads, as well as comonads and related structures, exist much more generally in programming languages; an exposition is in (Harper). For an account of the use of monads in industry see Benton15, pp. 11-12.\n\nFor instance when the monad $T(-)$ forms product types $T(X) \\coloneqq X \\times Q$ with some fixed type $Q$ that carries the structure of a monoid, then a Kleisli function $f : X \\to Y \\times Q$ may be thought of as a function $X \\to Y$ that produces a side effect output of type $Q$. The Kleisli composition of two functions $f \\colon X \\to Y \\times Q$ and $g \\colon Y \\to Z \\times Q$ then not only evaluates the two programs in sequence but also combines their $Q$-output using the monoid operation of $Q$; so if $f x = (y,q)$ and $g y = (z,q')$ then the final result of $(g \\circ f)(x)$ will be $(z, q q')$. For example, $Q$ might be the set of strings of characters, and the monoid operation that of concatenation of strings (i.e. $Q$ is the free monoid on the type of characters). If the software is designed such that values of type $Q$ computed in this way appear on the user’s screen or are written to memory, then this is a way to encode input/output in functional programming (see the IO monad? below).\n\nBut monads have plenty of further uses. They are as ubiquituous (sometimes in disguise) in computer science as monads in the sense of category theory are (sometimes in disguise) in category theory. This is no coincidence, see Relation to monads in category theory below.\n\n### Relation to monads in category theory\n\nIn computer science, a programming language may be formalised or studied by means of a category, called the syntactic category $\\mathcal{C}$, whose\n\n• objects$X \\in \\mathcal{C}$ are the types of the language,\n\n• morphisms$X \\to Y$ are the terms or programs (or an equivalence class of such) that takes a value of type $X$ as input and returns a value of type $Y$.\n\nThis point of view (see computational trinitarianism) is particularly useful when studying purely functional programming languages.\n\nUnder this relation between type theory and category theory monads on the type system in the sense of computer science are monads in the sense of category theory, being certain endofunctors\n\n$T \\colon \\mathcal{C} \\longrightarrow \\mathcal{C}$\n\non the syntactic category. This functor\n\n1. sends each type, hence object $X \\in \\mathcal{C}$ to another object $T(X)$;\n\n2. the unit natural transformation $\\epsilon \\colon Id_{\\mathcal{C}} \\Rightarrow T$ of the monad $T$ provides for each type $X$ a component morphism $pure_X : X \\to T(X)$;\n\n3. the multiplication natural transformation $\\mu \\colon T \\circ T \\Rightarrow T$ of the monad provides for each object $X$ a morphism $\\mu_X : T(T(X)) \\to T(X)$ which induces the Kleisli composition by the formula\n\n\\begin{aligned} (g \\circ f) &\\coloneqq (Y \\stackrel{g}{\\to} T(Z)) \\circ_{Kleisli} (X \\stackrel{f}{\\to} T(Y)) \\\\ & \\coloneqq X \\stackrel{f}{\\to} T(Y) \\stackrel{T(g)}{\\to} T(T(Z)) \\stackrel{\\mu(Z)}{\\to} T Z \\end{aligned} \\,,\n\nHere the morphism $T(g)$ in the middle of the last line makes use of the fact that $T(-)$ is indeed a functor and hence may also be applied to morphisms / functions between types. The last morphism $\\mu(Z)$ is the one that implements the “$T$-computation”.\n\nThe monads arising this way in computer science are usually required also to interact nicely with the structure of the programming language, as encoded in the structure of its syntactic category; in most cases, terms of the language will be allowed to take more than one input, so the category $\\mathcal{C}$ will be at least monoidal, and the corresponding kind of ‘nice’ interaction corresponds to the monad’s being a strong monad.\n\nThe ‘bind’ operation is a means of describing multiplication on such a strong monad $M$. It is a term of the form $M A \\to (M B)^A \\to M B$, which is equivalent to a map of the form $M A \\times M B^A \\to M B$. It is the composite\n\n$M A \\times M B^A \\stackrel{strength}{\\to} M(A \\times M B^A) \\stackrel{M eval_{A, M B}}{\\to} M M B \\stackrel{m B}{\\to} M B$\n\nwhere $m \\colon M M \\to M$ is the monad multiplication.\n\n## Examples\n\nVarious monads are definable in terms of the the standard type-forming operations (product type, function type, etc.). These include the following.\n\n• A functional program with input of type $X$, output of type $Y$ and mutable state $S$ is a function (morphism) of type $X \\times S \\longrightarrow Y \\times S$. Under the (Cartesian product $\\dashv$ internal hom)-adjunction this is equivalently given by its adjunct, which is a function of type $X \\longrightarrow [S, S \\times Y ]$. Here the operation $[S, S\\times (-)]$ is the monad induced by the above adjunction and this latter function is naturally regarded as a morphism in the Kleisli category of this monad. This monad $[S, S\\times (-)]$ is called the state monad for mutable states of type S.\n\n• The maybe monad is the operation $X \\mapsto X \\coprod \\ast$. The idea here is that a function $X \\longrightarrow Y$ in its Kleisli category is in the original category a function of the form $X \\longrightarrow Y \\coprod \\ast$ so either returns indeed a value in $Y$ or else returns the unique element of the unit type/terminal object $\\ast$. This is then naturally interpreted as “no value returned”, hence as indicating a “failure in computation”.\n\n• The continuation monad for a given type $S$ acts by $X \\mapsto [[X,S],S]$.\n\n• A number of further monads are similarly definable in terms of standard type-forming operations, such as the reader monad and the writer comonad.\n\nGiven a type $W$, then the reader monad is the operation of forming the function type $[W,-] = (W\\to (-))$; the writer comonad is the operation of forming the product type $W\\times (-)$ and the composite of writer followed by reader is the state monad $[W, W \\times (-)]$.\n\nWhen $W$ carries the structure of a monoid object then writer also inherits the structure of a monad (on top of being a comonad) and converse for reader.\n\nOther monads may be supplied “axiomatically” by the programming language, This includes\n\nExamples of (co)monads in (homotopy) type theory involve in particular modal operators as they appear in\n\nFor an approach to composing monads, see\n\nAnother approach to modelling side effects in functional programming languages are\n\nFree monads in computer science appear in the concepts of\n\nOther generalizations are\n\nThere is also\n\n### General\n\nThe original reference for monads as ‘notions of computation’ is\n\n• Eugenio Moggi, Notions of computation and monads, Information and Computation, 93(1), 1991. (pdf)\n\nThe impact of Moggi’s work is assessed and a case for Lawvere theories is made in\n\n• Martin Hyland, John Power, The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads, Electronic Notes in Theoretical Computer Science (ENTCS) archive Volume 172, April, 2007 Pages 437-458 (pdf)\n\nEffects treated this way are known as algebraic effects.\n\nExpositions of monads in computer science include\n\n• Philip Wadler, Comprehending Monads, in Conference on Lisp and functional programming, ACM Press, 1990 (pdf)\n\n• Philip Wadler, Monads for functional programming in Lecture notes for the Marktoberdorf Summer School on Program Design Calculi, Springer Verlag 1992\n\n• Philip Mulry?, Monads in semantics , ENTCS 14 (1998) pp.275-286.\n\n• John Hughes, section 2 of Generalising Monads to Arrows, Science of Computer Programming (Elsevier) 37 (1-3): 67–111. (2000) (pdf)\n\n• Robert Harper, Of course ML Has Monads! (2011) (web)\n\n• Nick Benton, Categorical Monads and Computer Programming, (pdf)\n\n• Emily Riehl, A categorical view of computational effects, 2017 (pdf)\n\nand an exposition of category theory and monads in terms of Haskell is in\n\nA comparison of monads with applicative functors (also known as idioms) and with arrows (in computer science) is in\n\n• Exequiel Rivas?, Relating Idioms, Arrows and Monads from Monoidal Adjunctions, (arXiv:1807.04084)" ]

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[ "", null, "The CP series SCR power controllers are multi-zone power controllers that can be configured for phase angle fired, zero voltage switched or on-off solid state contactor control of directly connected electric heaters. The CP will not control transformers or motors. This is accomplished by phase angle firing, or variable time based zero voltage switching a pair of inversely connected SCR's. Up to eight zones available on a single chassis. Single phase and three phase options.\n1 - 13 of 13 | Results Per Page | View | Unit of Measure\n1\n\n## Control Signal\n\nN/A 3CP-24-30, Zone 3 CP Series SCR Power Controller N/A 240 VAC 50/60 Hz N/A 30 AMPS N/A 0 to 97% of Input Voltage Phase Angle N/A 4 to 20 mA at 1.5 volts DC per zone\nN/A 3CP-24-40, Zone 3 CP Series SCR Power Controller N/A 240 VAC 50/60 Hz N/A 40 AMPS N/A 0 to 97% of Input Voltage Phase Angle N/A 4 to 20 mA at 1.5 volts DC per zone\nN/A 3CP-24-50, Zone 3 CP Series SCR Power Controller N/A 240 VAC 50/60 Hz N/A 50 AMPS N/A 0 to 97% of Input Voltage Phase Angle N/A 4 to 20 mA at 1.5 volts DC per zone\nN/A 3CP-24-70, Zone 3 CP Series SCR Power Controller N/A 240 VAC 50/60 Hz N/A 70 AMPS N/A 0 to 97% of Input Voltage Phase Angle N/A 4 to 20 mA at 1.5 volts DC per zone\nN/A 3CP-24-100, Zone 3 CP Series SCR Power Controller N/A 240 VAC 50/60 Hz N/A 100 AMPS N/A 0 to 97% of Input Voltage Phase Angle N/A 4 to 20 mA at 1.5 volts DC per zone\nN/A 3CP-48-30, Zone 3 CP Series SCR Power Controller N/A 480 VAC 50/60 Hz N/A 30 AMPS N/A 0 to 97% of Input Voltage Phase Angle N/A 4 to 20 mA at 1.5 volts DC per zone\nN/A 3CP-48-40, Zone 3 CP Series SCR Power Controller N/A 480 VAC 50/60 Hz N/A 40 AMPS N/A 0 to 97% of Input Voltage Phase Angle N/A 4 to 20 mA at 1.5 volts DC per zone\nN/A 3CP-48-50, Zone 3 CP Series SCR Power Controller N/A 480 VAC 50/60 Hz N/A 50 AMPS N/A 0 to 97% of Input Voltage Phase Angle N/A 4 to 20 mA at 1.5 volts DC per zone\nN/A 3CP-48-70, Zone 3 CP Series SCR Power Controller N/A 480 VAC 50/60 Hz N/A 70 AMPS N/A 0 to 97% of Input Voltage Phase Angle N/A 4 to 20 mA at 1.5 volts DC per zone\nN/A 3CP-48-100, Zone 3 CP Series SCR Power Controller N/A 480 VAC 50/60 Hz N/A 100 AMPS N/A 0 to 97% of Input Voltage Phase Angle N/A 4 to 20 mA at 1.5 volts DC per zone\nN/A 3CP-48-150, Zone 3 CP Series SCR Power Controller N/A 480 VAC 50/60 Hz N/A 150 AMPS N/A 0 to 97% of Input Voltage Phase Angle N/A 4 to 20 mA at 1.5 volts DC per zone\nN/A 3CP-48-225, Zone 3 CP Series SCR Power Controller N/A 480 VAC 50/60 Hz N/A 225 AMPS N/A 0 to 97% of Input Voltage Phase Angle N/A 4 to 20 mA at 1.5 volts DC per zone\nN/A 3CP-48-600, Zone 3 CP Series SCR Power Controller N/A 480 VAC 50/60 Hz N/A 600 AMPS N/A 0 to 97% of Input Voltage Phase Angle N/A 4 to 20 mA at 1.5 volts DC per zone\n1 - 13 of 13 | Results Per Page | View | Unit of Measure\n1", null, "" ]

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[ "# How is conditional main effect interpreted when there is interaction?\n\n#### Tim_95\n\n##### New Member\nI have a question about multiple regression. May I kindly ask how should I interpret the conditional main effect when the interaction is 0 and the coefficients have opposite signs, more specifically if one of the interaction term contains zero such as angle or time. Please see an example representing my problem below,\n\nz= b0+b1*X+b2*Y-b3*X*Y\nY (time) and X are continues variables\n\nIf I am not mistaken, we cannot interpret an isolated main effect, when there is a significant interaction; however, we can conditionally interpret in a whole model . If we check the effect of X on z when the time is different than 0 and and equals to zero, the equations then becomes as follow,\n\nz1= b0+b1*X+b2*Time-b3*X*Time\nz1=b0+b1*X+b2-b3*X -> y1=b0+(b1-b3*Time)*X+b2*Time\n\nThe effect of X, while increasing by one unit, on z1 is b1-b3*Time. So as time increases the effect is moving to more negative side.\n\nz2= b0+b1*X+b2*Time(0)-b3*X*Time (0)\nz2=b0-b1*X\n\nThe effect of X, while increasing by one unit, on z2 is positive b1 and it actually increase the z2. What does this practically mean? Or, should we conclude that as the Time increases the effect of X on Z1 is decreasing b1-b3*Time and you cannot individually check each time point but treat it as continues ?\n\nLast question, is it important if main effects here X and Time are significant or not if interaction is significant." ]

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[ "# Compiling Cooperative Task Management to Continuations\n\nConference paper\nPart of the Lecture Notes in Computer Science book series (LNCS, volume 8161)\n\n## Abstract.\n\nAlthough preemptive concurrency models are dominant for multi-threaded concurrency, they may be criticized for the complexity of reasoning because of the implicit context switches. The actor model and cooperative concurrency models have regained attention as they encapsulate the thread of control. In this paper, we formalize a continuation-based compilation of cooperative multitasking for a simple language and prove its correctness.\n\n## Keywords\n\nCooperative Multitasking Concurrency Model Concurrent Object Groups (COG) Original Entry Point Guard Expression\nThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.\n\n## 1 Introduction\n\nIn a preemptive concurrency model, threads may be suspended and activated at any time. While preemptive models are dominant for multi-threaded concurrency, they may be criticized for the complexity of reasoning because of the implicit context switches. The programmer often has to resort to low-level synchronization primitives, such as locks, to prevent unwanted context switches. Programs written in such a way tend to be error-prone and are not scalable. The actor model  addresses this issue. Actors encapsulate the thread of control and communicate with each other by sending messages. They are also able to call blocking operations such as sleep, await and receive, reminiscent of cooperative multi-tasking. Erlang and Scala actors support actor-based concurrency models.\n\nCreol  and ABS  combine a message-passing concurrency model and a cooperative concurrency model. In Creol, each object encapsulates a thread of control and objects communicate with each other using asynchronous method calls. Asynchronous method calls, instead of messages-passing, provide a type-safe communication mechanism and are a good match for object-oriented languages [3, 4]. ABS generalizes the concurrency model of Creol by introducing concurrent object groups  as the unit of concurrency. The concurrency model of ABS can be split in two: in one layer, we have local, synchronous and shared-memory communication1 in one concurrent object group (COG) and on the second layer we have asynchronous message-based concurrency between different concurrent object groups as in Creol. The behavior of one COG is based on the cooperative multitasking of external method invocations and internal method activations, with concrete scheduling points where a different task may get scheduled. Between different COGs only asynchronous method calls may be used; different COGs have no shared object heap. The order of execution of asynchronous method calls is not specified. The result of an asynchronous call is a future; callers may decide at run-time when to synchronize with the reply from a call. Asynchronous calls may be seen as triggers that spawn new method activations (or tasks) within objects. Every object has a set of tasks that are to be executed (originating from method calls). Among these, at most one task of all the objects belonging to one COG is active; others are suspended and awaiting execution. The concurrency models of Creol and ABS are designed to be suitable in the distributed setting, where one COG executes on its own (virtual) processor in a single node and different COGs may be executed on different nodes in the network.\n\nIn this paper, we are interested in the compilation of cooperative multi-tasking into continuations, motivated to execute a cooperative multi-tasking model on the JVM platform, which employs a preemptive model. The basic idea of using continuations to manage the control behavior of the computation has been known from 80’s [6, 12], and is still considered as a viable technique [1, 9, 11]. This is particularly so, if the programming language supports first-class continuations, as in the case of Scala, and hence one can obviate manual stack management. The contribution of the paper is a correctness proof of such a compilation scheme. Namely, we create a simplified source language, by extending the While language with (synchronous) procedure calls and operations for cooperative multi-tasking (i.e., blocking operations and creation of new tasks) and define a compilation function from the source language into the target language, which extends While with continuation operations—the target language is sequential. We then prove that the compilation preserves the operational behavior from the source language to the target language.\n\nThe remainder of the paper is organized as follows. We define the source language and its operational semantics in the next section, and the target language and its operational semantics in Section 3. In Section 4, we present the compilation function from the source language to the target language and, in Section 5 we prove its correctness. We conclude in Section 6.", null, "Fig. 1 Syntax of the source language\n\n## 2 Source Language\n\nIn Figure 1, we define the syntax for the source language. We use the overline notation to denote sequences, with $$\\epsilon$$ denoting an empty sequence. It is the While language extended with (local) variable definitions, $$\\mathtt {var}~ x = e$$, procedure calls $$f(\\overline{e})$$, the await statement $$\\mathtt {await}~ e$$, creation of a new task $$\\mathtt{spawn } ~ f ~ \\overline{e}$$, and the return statement $$\\mathtt {return}$$. For simplicity, we syntactically distinguish local variable assignment $$x := e$$ and global variable assignment $$u := e$$. The statement $$\\mathtt {var}~ x = e$$ defines a (task) local variable $$x$$ and initializes it with the value of $$e$$. The statement $$f(\\overline{e})$$ invokes the procedure $$f$$ with arguments $$\\overline{e}$$, to be executed within the same task. The procedure does not return the result to the caller, but may store the result in a global variable. The statement $$\\mathtt {await}~ e$$ suspends the execution of the current task, which can be resumed when the guard expression $$e$$ evaluates to true. The statement $$\\mathtt{spawn } ~ f ~ \\overline{e}$$ spawns a new task, which executes the body of $$f$$ with arguments $$\\overline{e}$$. (Hence, in contrast to procedure calls, which are synchronous, $$\\mathtt{spawn } ~ f ~ \\overline{e}$$ is like an asynchronous procedure call executed in a new task.) The $$\\mathtt {return}$$ statement is a runtime construct, not appearing in the source program, and will be explained later.\n\nWe assume disjoint supplies of local variables (ranged over by $$x$$), global variables (ranged over by $$u$$), and procedure names (ranged over by $$f$$). We assume a set of (pure) expressions, whose elements are ranged over by $$e$$. We assume the set of values to be the integers, non-zero integers counting as truth and zero as falsity. The metavariable $$v$$ ranges over values. We have two kinds of states – local states and global states. A local state, ranged over by $$\\rho$$, maps local variables to values; a global state, ranged over by $$\\sigma$$, maps global variables to values. We denotes by $$\\emptyset$$ an empty mapping, whose domain is empty. Communication between different tasks is achieved via global variables. For simplicity, we assume a fixed set of global variables. The notation $$\\rho [x\\mapsto v]$$ denotes the update of $$\\rho$$ with $$v$$ at $$x$$, when $$x$$ is in the domain of $$\\rho$$. If $$x$$ is not in the domain, it denotes a mapping extension. The notation $$\\sigma [u\\mapsto v]$$ denotes similar. We assume given an evaluation function $$[\\![e ]\\!]_ {(\\rho ,\\sigma )}$$, which evaluates $$e$$ in the local state $$\\rho$$ and the global state $$\\sigma$$. We write $$(\\rho ,\\sigma ) \\models e$$ and $$(\\rho ,\\sigma ) \\not \\models e$$ to denote that $$e$$ is true, resp. false with respect to $$\\rho$$ and $$\\sigma$$. A stack $$\\varPi$$ is a non-empty list of local states, whose elements are separated by semicolons. A stack grows leftward, i.e., the leftmost element is the topmost element.\n\nA program $$P$$ consists of a procedure environment $${\\mathrm{env }}_F$$ which maps procedure names to pairs of a formal argument list and a statement, and a global state which maps global variables to their initial values. The entry point of the program will be the procedure named main.\n\nWe define the operational semantics of the source language as a transition system on configurations, in the style of structural operational semantics. A configuration $${ cfg }$$ consists of an active task identifier $$n$$, a global variable mapping $$\\sigma$$ and a set of tasks $$\\varTheta$$. A task has an identifier and may be in one of the three forms: a triple $$\\langle e, S, \\varPi \\rangle$$, representing a task that is awaiting to be scheduled, where $$e$$ is the guard expression, $$S$$ the statement and $$\\varPi$$ its stack; or, a pair $$\\langle S, \\varPi \\rangle$$, representing the currently active task; or, a singleton $$\\langle \\varPi \\rangle$$, representing a terminated task.\n\\begin{aligned} \\begin{array}{lcl} Configuration &{} { cfg }&{}{:}{:}{=}\\ n, \\sigma \\triangleright \\varTheta \\\\ Task~sets &{} \\varTheta &{}{:}{:}{=}\\ n\\langle e, S, \\varPi \\rangle \\mid n\\langle S, \\varPi \\rangle \\mid n\\langle \\varPi \\rangle \\mid \\varTheta \\parallel \\varTheta \\end{array} \\end{aligned}\nThe order of tasks in the task set is irrelevant: the parallel operator $$\\parallel$$ is commutative and associative. Formally, we assume the following structural equivalence:\n\\begin{aligned} \\varTheta \\equiv \\varTheta \\qquad \\varTheta \\parallel \\varTheta ' \\equiv \\varTheta ' \\parallel \\varTheta \\qquad \\varTheta \\parallel (\\varTheta ' \\parallel \\varTheta '') \\equiv (\\varTheta \\parallel \\varTheta ') \\parallel \\varTheta '' \\end{aligned}\n\nTransition rules in the semantics are in the form $${\\mathrm{env }}_F \\vdash { cfg }\\rightarrow { cfg }'$$, shown in Figure 2. The first two rules (S-Cong and S-Equiv) deal with congruence and structural equivalence. The rules for assignment, $$\\mathtt {skip}$$, if-then-else and while are self-explanatory. For instance, in the rule S-Assign-Local, the task is of the form $$n\\langle S, \\varPi '\\rangle$$ where $$S = x:= e$$ and $$\\varPi ' = \\rho ;\\varPi$$. Note that the topmost element of the stack $$\\varPi$$ is the current local state. The rules for sequential composition may deserve some explanation. If the first statement $$S_1$$ suspends guarded by $$e$$ in the stack $$\\varPi '$$ with the residual statement $$S'_1$$ to be run when resumed, then the entire statement $$S_1;S_2$$ suspends in $$\\langle e, S'_1;S_2, \\varPi '\\rangle$$, where the residual statement now contains the second statement $$S_2$$ (S-Seq-Grd). If $$S_1$$ terminates in $$\\varPi '$$, then $$S_2$$ will run next in $$\\varPi '$$ (S-Seq-Fin). Otherwise, $$S_1$$ transfers to $$S'_1$$ with the stack $$\\varPi '$$, so that $$S_1;S_2$$ transfers to $$S'_1;S_2$$ with the same stack (S-Seq-Step). The await statement immediately suspends (S-Await) the currently active task, enabling us to switch to some other task in accordance to the scheduling rules. An example of the await statement (and the scheduling rules) at work can be found in the example in Figure 3. The statement $$\\mathtt{spawn } ~ f ~ \\overline{e}$$ creates a new task $$n'\\langle \\mathtt {true} , S, [\\overline{x} \\mapsto \\overline{v}]\\rangle$$ with $$n'$$ a fresh identifier (S-Spawn). The caller task continues to be active. The newly created task is suspended, guarded by $$\\mathtt {true}$$, and may get scheduled at scheduling points by the scheduling rules (see below). Procedure invocation $$f(\\overline{e})$$ evaluates the arguments $$\\overline{e}$$ in the current state, pushes into the stack the local state $$[\\overline{x} \\mapsto \\overline{v}]$$, mapping the formal parameters to the actual arguments, and transfers to $$S;\\mathtt {return}$$, where $$S$$ is the body of $$f$$ (S-Call). The $$\\mathtt {return}$$ statement pops the topmost element from the stack (S-Return). The local variable definition $$\\mathtt {var}~ x = e$$ extends the current local state with the newly defined variable and initializes it with the value of $$e$$ (S-Var).\n\nThe last three rules deal with scheduling. If the current active task has terminated, then a new task whose guard evaluates to true is chosen to be active (S-Sched-Fin). When the active task suspends, a scheduling point is reached. The rule (S-Sched-Same) considers the case in which the same task is scheduled; the rule (S-Sched-Other) considers the case in which a different task is scheduled.", null, "Fig. 3 The full execution trace of the example program", null, "Fig. 4 Example of a derivation in the source language\nAs an example, we will look at a program containing one global variable $$u$$ with the initial value $$0$$ and the following procedures:\n\\begin{aligned} \\mathsf{f }&\\mapsto u := 1 \\\\ \\mathsf{main }&\\mapsto u := 3; \\mathtt{spawn } ~ \\mathsf {f} ~ \\epsilon ; \\mathtt {await}~ u = 1; u := 2 \\end{aligned}\nA detailed step, showing the full derivation, can be seen in Figure 4. A full execution trace, showing all intermediate configurations, is shown in Figure 3.\n\n## 3 Target Language\n\nWe proceed to the target language. In Figure 5, we present the syntax of the target language. Expressions of the target language contain, besides pure expressions, continuations $$[S, \\varPi ]$$, which are pairs of a statement $$S$$ and a stack $$\\varPi$$, and support for guarded (multi)sets: collections which contain pairs of an expression and a value. The expression stored with each element is called a guard expression, and is evaluated when we query the set: only elements whose guard expressions hold may be returned. There are five expressions in the language to work with guarded sets: an empty set $$\\emptyset$$, checking whether a set is empty ($$\\mathtt{isEmpty } ~ e_s$$), adding an element ($$\\mathtt{add } ~ e_s ~ e_g ~ e$$), fetching an element ($$\\mathtt{get } ~ e_s$$) and removing an element ($$\\mathtt{del } ~ e_s ~ e$$).", null, "Fig. 5 Syntax of the target language\n\nSimilar to the source language, for the target language we extend While with local variable definitions and procedure calls. We also add delimited control operators, $$\\mathtt{shift~ } k ~ \\{ S \\}$$, $$\\mathtt{reset~ } \\{ S \\}$$, $$\\mathtt{invoke } ~k$$ . The statement $$\\mathtt{shift~ } k ~ \\{ S \\}$$ captures the rest of the computation, or continuation, up to the closest surrounding $$\\mathtt{reset~ } \\{ \\}$$, binds it to $$k$$, and proceeds to execute $$S$$. In $$\\mathtt{shift~ } k ~ \\{ S \\}$$, $$k$$ is a binding occurrence, whose scope is $$S$$. Hence, the statement $$\\mathtt{reset~ } \\{ S \\}$$ delimits the captured continuation. The statement $$\\mathtt{invoke } ~k$$ invokes, or jumps into, the continuation bound to the variable $$k$$. The statement $$\\mathtt{R~ } \\{ S \\}$$, where $$\\mathtt {R}$$ is a new constant, is a runtime construct to be explained later.\n\nThe target language is sequential and, unlike the source language, it contains no explicit support for parallelism. Instead, we provide building blocks – continuations and guarded sets – that are used to switch between tasks and implement an explicit scheduler in Section 4.\n\nWe assume given an evaluation function $$[\\![e ]\\!]_ {(\\varPi ,\\sigma )}$$ for pure expressions, which evaluates $$e$$ with respect to the stack $$\\varPi$$ (the evaluation only looks at the current local state, which is the topmost element of $$\\varPi$$) and the global state $$\\sigma$$. In Figure 6, the evaluation function is extended to operations for guarded sets.", null, "Fig. 6 Semantics of the target language\n\nWe define an operational semantics for the target language as a reduction semantics over configurations, using evaluation contexts. A configuration $$\\langle S, \\varPi , \\sigma \\rangle$$ is a triple of a statement $$S$$, a stack $$\\varPi$$ and a global state $$\\sigma$$.\n\nEvaluation contexts $$E$$ are statements with a hole, specifying where the next reduction may occur. They are defined by\n\\begin{aligned} E\\ {:}{:}{=}\\ [] \\mid E; S \\mid \\mathtt{R~ } \\{ E \\} \\end{aligned}\nWe denote by $$E[S]$$ the statement obtained by placing $$S$$ in the hole of $$E$$.\nWe define basic reduction rules in Figure 6. $$\\mathtt{reset~ } \\{ S \\}$$ inserts a marker $$\\dagger$$ into the stack, just below the current state, and reduces to $$\\mathtt{R~ } \\{ S \\}$$ to continue the execution of $$S$$ (T-Reset). We use a marker to delimit the portion of the stack captured by $$\\mathtt{shift }$$ and to align the stack when exiting from $$\\mathtt{R~ } \\{ \\}$$. The runtime construct $$\\mathtt{R~ } \\{ \\}$$ is used to record that the marker has been set. $$\\mathtt{shift~ } k ~ \\{ S \\}$$ captures the rest of the execution up to and including the closest surrounding $$\\mathtt{R~ } \\{ \\}$$ together with the corresponding portion of the stack, binds it to a fresh variable $$k'$$ in the local state, and continues with the statement $$S'$$ obtained by substituting $$k$$ by $$k'$$ in $$S$$ (T-Shift). The surrounding $$\\mathtt{R~ } \\{ \\}$$ is kept intact. $$F$$ is an evaluation context that does not intersect $$\\mathtt{R~ } \\{ \\}$$, formally,\n\\begin{aligned} F\\ {:}{:}{=}\\ [] \\mid F; S \\end{aligned}\nNote that $$\\mathtt{shift~ } k ~ \\{ S \\}$$ captures the stack up to and including the topmost $$\\dagger$$, which has been inserted by the closest surrounding reset. Once the body of $$\\mathtt{R~ } \\{ \\}$$ terminates, i.e., reduces to $$\\mathtt {skip}$$, then we remove the $$\\mathtt{R~ } \\{ \\}$$ and pop the stack until the topmost $$\\dagger$$, but leaving the state just above $$\\dagger$$ in the stack (T-R). $$\\mathtt{invoke } ~k$$ invokes the continuation bound to $$k$$ (T-Invoke). Namely, if $$k$$ is bound to $$[S, \\varPi ']$$ in the local or global state, then the statement reduces to $$S; \\mathtt {return}$$ and the stack $$\\varPi '$$ is pushed into the current stack. $$S$$ must be necessarily of the form $$\\mathtt{R~ } \\{ S' \\}$$, where $$S'$$ does not contain $$\\mathtt{R }$$, and $$\\varPi '$$ contains exactly one $$\\dagger$$ at the bottom. When exiting from the $$\\mathtt{R~ } \\{ \\}$$, the state immediately above $$\\dagger$$ in $$\\varPi '$$ will be left in the stack, which is popped by the trailing $$\\mathtt {return}$$. An example of how to capture and invoke a continuation is shown in Figure 7. In the example, we assume that the variables $$u$$ and $$u'$$ are global.", null, "Fig. 7 Capturing and invoking a continuation\n\nProcedure call $$f (\\overline{e})$$ reduces to $$S; \\mathtt {return}$$ where $$S$$ is the body of the procedure $$f$$, and pushes a local state $$[\\overline{x} \\mapsto \\overline{v}]$$, binding procedure’s formal arguments to actual arguments, into the stack (T-Call). The trailing $$\\mathtt {return}$$ ensures that, once the execution of $$S; \\mathtt {return}$$ terminates, the stack is aligned to the original $$\\varPi$$. $$\\mathtt {return}$$ pops the topmost element from the stack (T-Return). The remaining rules are self-explanatory.\n\nGiven the basic reduction rules, we now define a standard reduction, denoted by $$\\mapsto$$, by\n\\begin{aligned} \\frac{{\\mathrm{env }}_F \\vdash \\langle S, \\varPi , \\sigma \\rangle \\rightarrow \\langle S', \\varPi ', \\sigma ' \\rangle }{{\\mathrm{env }}_F \\vdash \\langle E [ S ], \\varPi , \\sigma \\rangle \\mapsto \\langle E [ S' ], \\varPi ', \\sigma ' \\rangle } \\end{aligned}\nstating that the configuration $$\\langle S, \\varPi , \\sigma \\rangle$$ standard reduces to $$\\langle S', \\varPi ', \\sigma '\\rangle$$ if there exist an evaluation context $$E$$ and statement $$S_0$$ and $$S'_0$$ such that $$S = E[S_0]$$ and $$S' = E[S'_0]$$ and $${\\mathrm{env }}_F \\vdash \\langle S_0, \\varPi , \\sigma \\rangle \\rightarrow \\langle S'_0, \\varPi ', \\sigma '\\rangle$$. The standard reduction is deterministic.\n\n## 4 Compilation\n\nWhen compiling a program $$P$$ into the target language, we compile expressions and statements according to the scheme shown in Figure 8. Expressions are translated into the target language as-is, and statements that have a corresponding equivalent in the target language are also translated in a straightforward manner. The two statements that have no direct correspondence in the target language are $$\\mathtt{await }$$ and $$\\mathtt{spawn }$$. We look at how these statements are translated and how they interact with the scheduler later.", null, "Fig. 8 Compilation of source programs\nThe central idea of the compilation scheme is to use continuations to handle the suspension of tasks, and have an explicit scheduler (for brevity, in the examples we use $$Sched$$ to denote the scheduler), shown in Figure 9. The control will pass to the scheduler every time a task either suspends or finishes, and the scheduler will pick up a new task to execute. During runtime, we also use a global variable $$T$$, which we assume not to be used by the program to be compiled. The global variable $$T$$ stores the task set, corresponding to $$\\varTheta$$ in the source semantics, that contains all the tasks in the system. The tasks are stored as continuations with guard expressions.", null, "Fig. 9 Scheduler\n\nThe scheduler loops until the task set is empty (all tasks have terminated), in each iteration picking a continuation from $$T$$ where the guard expression evaluates to $$\\mathtt {true}$$, removing it from $$T$$ and then invoking the continuation using $$\\mathtt{invoke } ~k$$. The body of the scheduler is wrapped in a $$\\mathtt {reset}$$, guaranteeing that when a task suspends, the capture will be limited to the end of the current task. After the execution is completed – either by suspension or by just finishing the work – the control comes back to the scheduler.\n\nSuspension ($$\\mathtt {await}~ e$$ in the source language) is compiled to a $$\\mathtt {shift}$$ statement. When evaluating the statement, the original computation until the end of the enclosing $$\\mathtt{R~ } \\{ \\}$$ will be captured and stored in the continuation $$k$$, and the original program is replaced with the body of the $$\\mathtt {shift}$$. The enclosing $$\\mathtt{R~ } \\{ \\}$$ guarantees that we capture only the statements up until the end of the current task, thus providing a facility to proceed with the execution of the task later. The body of the $$\\mathtt {shift}$$ statement simply takes the captured continuation, $$k$$, and adds it to the global task set, with the appropriate guard expression. After adding the continuation to the task set, the control passes back to the scheduler.\n\nProcedures in $${\\mathrm{env }}_F$$ will get translated into two different procedures for synchronous and asynchronous calls, as follows:\n\\begin{aligned} f_S&\\mapsto [\\![S ]\\!]\\\\ f_A&\\mapsto \\mathtt{reset~ } \\{ \\mathtt{shift~ } k ~ \\{ T := \\mathtt{add } ~ T ~ \\mathtt {true} ~ k \\}; [\\![S ]\\!] \\} \\end{aligned}\nWhen making an asynchronous call, the body of the procedure will be immediately captured in a continuation, added to the global task set, and the control passes back to the invoker via the usual synchronous call mechanism.\nThe entry point of a program in the source language, main, is a regular procedure and will get translated according to the usual rules into two procedures, $$\\mathsf {main} _A$$ and $$\\mathsf {main} _S$$. In the target language, we must invoke the scheduler, and thus we use a different entry point:\n\\begin{aligned} T := \\emptyset ; \\mathsf {main} _A (); Sched \\end{aligned}\nAfter initializing the task set to be empty, the first statement will add an asynchronous call to the original entry point of the program, and passes control to the scheduler. As there is only one task in the task set – the task that will invoke the original entry point – the scheduler will immediately proceed with that.\n\n## 5 Correctness\n\nIn this section, we prove that our compilation scheme is correct in the sense that it preserves the operational behavior from the source program into the (compiled) target program. Specifically, we prove that reductions in the source language are simulated by corresponding reductions in the target language. To do so, we extend the compilation scheme to configurations in Figure 10.", null, "Fig. 10 Compilation of configurations\n\nThe compilation scheme for configurations follows the idea of the compilation scheme detailed in Section 4. We have two compilation functions: $$[\\![\\cdot ]\\!]_2$$, which generates a task set from $$\\varTheta$$, and $$[\\![\\cdot ]\\!]$$, which generates a configuration in the target semantics.\n\nEvery suspended task in the task set $$\\varTheta$$ is compiled to a pair consisting of the compiled guard expression and a continuation that has been constructed from the original statement and stack. The statement is wrapped in a $$\\mathtt{R~ } \\{ \\}$$ block and we prepend a $$\\mathtt {skip}$$ statement, just as it would happen when a continuation is captured in the target language.\n\nIf the active task is finished or is suspended (but no new task has been scheduled yet), the generated configuration will immediately contain the scheduler. If the task has suspended, the task is compiled according to the previously described scheme and appended to $$T$$. Active tasks are wrapped in two $$\\mathtt{R~ } \\{ \\}$$ blocks and the stack $$\\varPi$$ is concatenated on top of the local state of the scheduler.\n\nWhen the scheduler invokes a continuation $$k$$, the continuation will stay in the local state of the scheduler until control comes back to the scheduler. This is unnecessary, as the value is never used after it has been invoked; furthermore, the variable is immediately assigned a new value after control passes back to the scheduler. Thus, as an optimization, we may switch to an alternative reduction rule for $$\\mathtt{invoke } ~k$$, which only allows a continuation to be used once, T-InvokeOnce, shown in Figure 11. Although the behavior of the program is equivalent under both versions, using the one-shot version also allows us to state the correctness theorem in a more concise and straightforward manner, as the local state of the scheduler will always be empty when we are currently executing some task. In the proof, we assume this rule to be used instead of the original T-Invoke rule.", null, "Fig. 11 Alternative rule for $$\\mathtt {invoke}$$\nThe following lemma states that the compilation of statements is compositional with respect to evaluation contexts, where evaluation contexts for the source language are defined inductively by\n\\begin{aligned} K := [] \\mid K; S. \\end{aligned}\n\n### Lemma 1.\n\n\\begin{aligned}{}[\\![K[S]]\\!]= [\\![K ]\\!]\\big [[\\![S ]\\!]\\big ] \\end{aligned}\n\n### Proof.\n\nBy induction on the structure of $$K$$. $$\\square$$\n\nThe correctness theorem below states that a one-step reduction in the source language is simulated by multiple-step reductions in the target language.\n\nAs an example, in Figure 12 we show the compiled form for both the initial and final configurations shown for the step in Figure 4 and in Figure 13, we show how to reach the compiled equivalent of the configuration in multiple steps in the target semantics.", null, "Fig. 12 Example of compiling a configuration", null, "Fig. 13 Reduction of the compiled configuration\n\n### Theorem 1.\n\nFor all configurations $${ cfg }_S$$ and $${ cfg }_S'$$ such that\n\\begin{aligned} {\\mathrm{env }}_F \\vdash { cfg }_S \\rightarrow { cfg }_S' \\end{aligned}\nholds, then the following must also hold:\n\\begin{aligned}{}[\\![{\\mathrm{env }}_F ]\\!]\\vdash [\\![{ cfg }_S ]\\!]\\mapsto ^+ [\\![{ cfg }_S' ]\\!]. \\end{aligned}\n\n### Proof.\n\nBy induction over the derivation, analyzing the step taken. The possible steps have one of the following forms:\n• Case\n\\begin{aligned} {\\mathrm{env }}_F \\vdash n, \\sigma \\triangleright n\\langle S, \\varPi \\rangle \\parallel \\varTheta \\rightarrow n', \\sigma ' \\triangleright n\\langle \\varPi ' \\rangle \\parallel \\varTheta ' \\end{aligned}\nRules matching this pattern are S-Assign-Local, S-Assign-Global, S-While-False, S-Spawn, S-Return, S-Var. As a representative example, we will look at S-Spawn in detail.\n\\begin{aligned} \\frac{{\\mathrm{env }}_F~f = (\\overline{x}, S) \\quad \\overline{v} = [\\![\\overline{e} ]\\!]_{(\\rho , \\sigma )}\\quad n' \\text { is fresh}}{{\\mathrm{env }}_F \\vdash n, \\sigma \\triangleright n\\langle \\mathtt{spawn } ~ f ~ \\overline{e}, \\rho ; \\varPi \\rangle \\rightarrow n, \\sigma \\triangleright n\\langle \\rho ; \\varPi \\rangle \\parallel n'\\langle \\mathtt {true} , S, [\\overline{x} \\mapsto \\overline{v}] \\rangle } \\end{aligned}\nIn this case, the source and target configurations are compiled to:\n\\begin{aligned}{}[\\![{ cfg }_S ]\\!]&= \\langle \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ f_A(\\overline{e}) \\}; \\mathtt {return} \\}; Sched , \\rho ; \\varPi \\dagger ; \\emptyset \\dagger , \\sigma [T \\mapsto [\\![\\varTheta ]\\!]_2]\\rangle \\\\ [\\![{ cfg }_S' ]\\!]&= \\langle Sched , \\emptyset , \\sigma [T \\mapsto [\\![\\varTheta ]\\!]_2 \\cup \\{(\\mathtt {true} , [\\mathtt{R~ } \\{ \\mathtt {skip} ; [\\![S ]\\!] \\}, [\\overline{x} \\mapsto \\overline{v}]\\dagger ])\\}]\\rangle \\end{aligned}\nLet the bottommost element of $$\\varPi$$ be $$\\rho '$$, where $$\\rho = \\rho '$$ if $$\\varPi$$ is empty. The compiled source configuration will reduce as follows:\n\\begin{aligned}&[\\![{\\mathrm{env }}_F ]\\!]\\vdash \\langle \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ f_A(\\overline{e}) \\}; \\mathtt {return} \\}; Sched , \\rho ; \\varPi \\dagger ; \\emptyset \\dagger , \\sigma [T \\mapsto [\\![\\varTheta ]\\!]_2]\\rangle \\\\&\\mapsto \\langle \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ \\mathtt{reset~ } \\{ \\mathtt{shift~ } k ~ \\{ T := \\mathtt{add } ~ T ~ \\mathtt {true} ~ k \\}; [\\![S ]\\!] \\}; \\mathtt {return} \\}; \\mathtt {return} \\}; Sched , \\\\&\\qquad \\qquad [\\overline{x} \\mapsto \\overline{v}]; \\rho ; \\varPi \\dagger ; \\emptyset \\dagger , \\sigma [T \\mapsto [\\![\\varTheta ]\\!]_2]\\rangle \\\\&\\mapsto \\langle \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ \\mathtt{shift~ } k ~ \\{ T := \\mathtt{add } ~ T ~ \\mathtt {true} ~ k \\}; [\\![S ]\\!] \\}; \\mathtt {return} \\}; \\mathtt {return} \\}; Sched , \\\\&\\qquad \\qquad [\\overline{x} \\mapsto \\overline{v}]\\dagger ; \\rho ; \\varPi \\dagger ; \\emptyset \\dagger , \\sigma [T \\mapsto [\\![\\varTheta ]\\!]_2]\\rangle \\\\&\\mapsto \\langle \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ T := \\mathtt{add } ~ T ~ \\mathtt {true} ~ k \\}; \\mathtt {return} \\}; \\mathtt {return} \\}; Sched , \\\\&\\qquad \\qquad [\\overline{x} \\mapsto \\overline{v}, k \\mapsto [\\mathtt{R~ } \\{ \\mathtt {skip} ; [\\![S ]\\!] \\}, [\\overline{x} \\mapsto \\overline{v}]\\dagger ]\\dagger ; \\rho ; \\varPi \\dagger ; \\emptyset \\dagger , \\sigma [T \\mapsto [\\![\\varTheta ]\\!]_2]\\rangle \\\\&\\mapsto \\langle \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ \\mathtt {skip} \\}; \\mathtt {return} \\}; \\mathtt {return} \\}; Sched , [\\overline{x} \\mapsto \\overline{v}, k \\mapsto [\\mathtt{R~ } \\{ \\mathtt {skip} ; [\\![S ]\\!] \\}, [\\overline{x} \\mapsto \\overline{v}]\\dagger ]\\dagger ; \\rho ; \\varPi \\dagger ; \\emptyset \\dagger , \\qquad \\qquad \\sigma [T \\mapsto [\\![\\varTheta ]\\!]_2 \\cup \\{(\\mathtt {true} , [\\mathtt{R~ } \\{ \\mathtt {skip} ; [\\![S ]\\!] \\}, [\\overline{x} \\mapsto \\overline{v}]\\dagger ])\\}]\\rangle \\\\&\\mapsto \\langle \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ \\mathtt {return} \\}; \\mathtt {return} \\}; Sched , [\\overline{x} \\mapsto \\overline{v}, k \\mapsto [\\mathtt{R~ } \\{ \\mathtt {skip} ; [\\![S ]\\!] \\}, [\\overline{x} \\mapsto \\overline{v}]\\dagger ]; \\rho ; \\varPi \\dagger ; \\emptyset \\dagger , MYAMP]\\qquad \\qquad \\sigma [T \\mapsto [\\![\\varTheta ]\\!]_2 \\cup \\{(\\mathtt {true} , [\\mathtt{R~ } \\{ \\mathtt {skip} ; [\\![S ]\\!] \\}, [\\overline{x} \\mapsto \\overline{v}]\\dagger ])\\}]\\rangle \\\\&\\mapsto \\langle \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ \\mathtt {skip} \\}; \\mathtt {return} \\}; Sched , \\rho ; \\varPi \\dagger ; \\emptyset \\dagger , \\sigma [T \\mapsto [\\![\\varTheta ]\\!]_2 \\cup \\{(\\mathtt {true} , [\\mathtt{R~ } \\{ \\mathtt {skip} ; [\\![S ]\\!] \\}, [\\overline{x} \\mapsto \\overline{v}]\\dagger ])\\}]\\rangle \\\\&\\mapsto \\langle \\mathtt{R~ } \\{ \\mathtt {return} \\}; Sched , \\rho '; \\emptyset \\dagger , \\sigma [T \\mapsto [\\![\\varTheta ]\\!]_2 \\cup \\{(\\mathtt {true} , [\\mathtt{R~ } \\{ \\mathtt {skip} ; [\\![S ]\\!] \\}, [\\overline{x} \\mapsto \\overline{v}]\\dagger ])\\}]\\rangle \\\\&\\mapsto \\langle \\mathtt{R~ } \\{ \\mathtt {skip} \\}; Sched , \\emptyset \\dagger , \\sigma [T \\mapsto [\\![\\varTheta ]\\!]_2 \\cup \\{(\\mathtt {true} , [\\mathtt{R~ } \\{ \\mathtt {skip} ; [\\![S ]\\!] \\}, [\\overline{x} \\mapsto \\overline{v}]\\dagger ])\\}]\\rangle \\\\&\\mapsto \\langle Sched , \\emptyset , \\sigma [T \\mapsto [\\![\\varTheta ]\\!]_2 \\cup \\{(\\mathtt {true} , [\\mathtt{R~ } \\{ \\mathtt {skip} ; [\\![S ]\\!] \\}, [\\overline{x} \\mapsto \\overline{v}]\\dagger ])\\}]\\rangle \\\\ \\end{aligned}\nThe configuration we obtain from evaluation is exactly equal to the compiled configuration, thus for this case our claim holds.\n• Case\n\\begin{aligned} {\\mathrm{env }}_F \\vdash n, \\sigma \\triangleright n\\langle S, \\varPi \\rangle \\parallel \\varTheta \\rightarrow n', \\sigma ' \\triangleright n\\langle e, S', \\varPi ' \\rangle \\parallel \\varTheta ' \\end{aligned}\nThere are only two possible rules: S-Seq-Grd and S-Await. In both cases, it must be that $$\\sigma = \\sigma '$$, $$\\varPi = \\varPi '$$, $$\\varTheta \\equiv \\varTheta '$$ and there exists some $$K$$ such that $$S = K[\\mathtt {await}~ e]$$ and $$S' = K [\\mathtt {skip} ]$$. Therefore, taking into account Lemma 1, the source and target configurations are compiled to:\n\\begin{aligned}{}[\\![{ cfg }_S ]\\!]&= \\langle \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ [\\![K ]\\!][[\\![\\mathtt {await}~ e ]\\!]] \\}; \\mathtt {return} \\}; Sched , \\varPi \\dagger ;\\emptyset \\dagger , \\sigma [T \\mapsto [\\![\\varTheta ]\\!]_2]\\rangle \\\\&= \\langle \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ [\\![K ]\\!][\\mathtt{shift~ } k ~ \\{ T := \\mathtt{add } ~ T ~ [\\![e ]\\!] ~ k \\}; \\mathtt {skip} ] \\}; \\mathtt {return} \\}; Sched , \\varPi \\dagger ;\\emptyset \\dagger , \\sigma [T \\mapsto [\\![\\varTheta ]\\!]_2]\\rangle \\\\ [\\![{ cfg }_S' ]\\!]&= \\langle Sched , \\emptyset , \\sigma [T \\mapsto [\\![\\varTheta ]\\!]_2 \\cup \\{([\\![e ]\\!], \\mathtt{R~ } \\{ [\\![K ]\\!][ \\mathtt {skip} ] \\}, \\varPi \\dagger )\\}\\rangle \\end{aligned}\nAn example of this reduction can be seen in Figure 13.\n• Case\n\\begin{aligned} {\\mathrm{env }}_F \\vdash n, \\sigma \\triangleright n\\langle S, \\varPi \\rangle \\parallel \\varTheta \\rightarrow n', \\sigma ' \\triangleright n\\langle S', \\varPi ' \\rangle \\parallel \\varTheta ' \\end{aligned}\nRules matching this pattern are S-Seq-Fin, S-Seq-Step, S-If-True, S-If-False, S-While-True, S-Call. In the case of S-Seq-Step, we know that $$S = S_0;S_1$$ and $$S' = S_0'; S_1$$. By induction hypothesis, we get that\n\\begin{aligned}{}[\\![{\\mathrm{env }}_F ]\\!]\\vdash [\\![n, \\sigma \\triangleright n\\langle S_0, \\varPi \\rangle \\parallel \\varTheta ]\\!]\\rightarrow [\\![n', \\sigma ' \\triangleright n\\langle S_0', \\varPi ' \\rangle \\parallel \\varTheta ' ]\\!]\\end{aligned}\nAs by the definition of the compilation function $$[\\![S ]\\!]= [\\![S_0 ]\\!]; [\\![S_1 ]\\!]$$ and $$[\\![S' ]\\!]= [\\![S_0' ]\\!]; [\\![S_1 ]\\!]$$, we obtain the needed result:\n\\begin{aligned}{}[\\![{\\mathrm{env }}_F ]\\!]\\vdash [\\![n, \\sigma \\triangleright n\\langle S_0; S_1, \\varPi \\rangle \\parallel \\varTheta ]\\!]\\rightarrow [\\![n', \\sigma ' \\triangleright n\\langle S_0'; S_1, \\varPi ' \\rangle \\parallel \\varTheta ' ]\\!]\\end{aligned}\nFor S-Seq-Fin, we know that $$S = S_0; S_1$$ and $$S' = S_1$$. Then the case follows by analyzing the step taken to reduce $$S_0$$.\n\nThe other cases are straightforward.\n\n• One of the following three:\n\\begin{aligned} {\\mathrm{env }}_F \\vdash n, \\sigma \\triangleright n\\langle \\varPi '\\rangle \\parallel n' \\langle e, S, \\varPi \\rangle \\parallel \\varTheta&\\rightarrow n', \\sigma \\triangleright n\\langle \\varPi '\\rangle \\parallel n'\\langle S, \\varPi \\rangle \\parallel \\varTheta \\\\ {\\mathrm{env }}_F \\vdash n, \\sigma \\triangleright n\\langle e', S', \\varPi '\\rangle \\parallel n' \\langle e, S, \\varPi \\rangle \\parallel \\varTheta&\\rightarrow n', \\sigma \\triangleright n\\langle e', S', \\varPi ' \\rangle \\parallel n'\\langle S, \\varPi \\rangle \\parallel \\varTheta \\\\ {\\mathrm{env }}_F \\vdash n, \\sigma \\triangleright n\\langle e, S, \\varPi \\rangle \\parallel \\varTheta&\\rightarrow n, \\sigma \\triangleright n\\langle S, \\varPi \\rangle \\parallel \\varTheta \\\\ \\end{aligned}\nThese three patterns match each of the scheduling rules. We will look only at the first one.\n\\begin{aligned} \\frac{(\\rho , \\sigma ) \\models e}{{\\mathrm{env }}_F \\vdash n, \\sigma \\triangleright n\\langle \\varPi ' \\rangle \\parallel n'\\langle e, S, \\rho ; \\varPi \\rangle \\rightarrow n', \\sigma \\triangleright n'\\langle S, \\rho ; \\varPi \\rangle \\parallel n\\langle \\varPi ' \\rangle }\\textsc {S-Sched-Fin} \\end{aligned}\n\\begin{aligned}{}[\\![{ cfg }_S ]\\!]&= \\langle Sched , \\emptyset , \\sigma [T \\mapsto \\{([\\![e ]\\!], [\\mathtt{R~ } \\{ \\mathtt {skip} ; [\\![S ]\\!] \\}, \\rho ; \\varPi \\dagger ])\\}]\\rangle \\\\ [\\![{ cfg }_S' ]\\!]&= \\langle \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ [\\![S ]\\!] \\}; \\mathtt {return} \\}; Sched , \\rho ; \\varPi \\dagger ; \\emptyset \\dagger , \\sigma [T \\mapsto \\emptyset ]\\rangle \\\\ \\end{aligned}\nThe initial configuration will reduce as (with some of the steps omitted):\n\\begin{aligned}&[\\![{\\mathrm{env }}_F ]\\!]\\vdash \\langle \\mathtt {While} {(\\lnot \\mathtt{isEmpty } ~ T)}\\mathtt {do} {\\mathtt{reset~ } \\{ k := \\mathtt{get } ~ T; T := \\mathtt{del } ~ T ~ k; \\mathtt{invoke } ~k \\}},\\\\&\\qquad \\qquad \\emptyset , \\sigma [T \\mapsto \\{([\\![e ]\\!], [\\mathtt{R~ } \\{ \\mathtt {skip} ; [\\![S ]\\!] \\}, \\rho ; \\varPi \\dagger ])\\}]\\rangle \\\\&\\mapsto \\langle \\mathtt{reset~ } \\{ k := \\mathtt{get } ~ T; T := \\mathtt{del } ~ T ~ k; \\mathtt{invoke } ~k \\}; {Sched}, \\\\&\\qquad \\qquad \\emptyset , \\sigma [T \\mapsto \\{([\\![e ]\\!], [\\mathtt{R~ } \\{ \\mathtt {skip} ; [\\![S ]\\!] \\}, \\rho ; \\varPi \\dagger ])\\}]\\rangle \\\\&\\mapsto \\langle \\mathtt{R~ } \\{ k := \\mathtt{get } ~ T; T := \\mathtt{del } ~ T ~ k; \\mathtt{invoke } ~k \\}; {Sched}, \\emptyset \\dagger , \\sigma [T \\mapsto \\{([\\![e ]\\!], [\\mathtt {skip} ; \\mathtt{R~ } \\{ [\\![S ]\\!] \\}, \\rho ; \\varPi \\dagger ])\\}]\\rangle \\\\&\\mapsto ^* \\langle \\mathtt{R~ } \\{ \\mathtt{invoke } ~k \\}; , [k \\mapsto [\\mathtt{R~ } \\{ \\mathtt {skip} ; [\\![S ]\\!] \\}, \\rho ; \\varPi \\dagger ]] \\dagger , \\sigma [T \\mapsto \\emptyset ]\\rangle \\\\&\\mapsto \\langle \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ \\mathtt {skip} ; [\\![S ]\\!] \\}; \\mathtt {return} \\}; {Sched}, \\rho ; \\varPi \\dagger ; \\emptyset \\dagger , \\sigma [T \\mapsto \\emptyset ]\\rangle \\\\&\\mapsto \\langle \\mathtt{R~ } \\{ \\mathtt{R~ } \\{ [\\![S ]\\!] \\}; \\mathtt {return} \\}; {Sched}, \\rho ; \\varPi \\dagger ; \\emptyset \\dagger , \\sigma [T \\mapsto \\emptyset ]\\rangle \\end{aligned}\n\n## 6 Conclusion\n\nIn this paper, we formalized a compilation scheme for cooperative multi-tasking into delimited continuations. For the source language, we extend While with procedure calls and operations for blocking and creation of new tasks. The target language extends While with shift/reset—the target language is sequential. We then proved that the compilation scheme is correct: reductions in the source language are simulated by corresponding reductions in the target language. We have implemented this compilation scheme in our compiler from ABS to Scala. The compiler covers a much richer language than our source language, including object-oriented features, and employs the experimental continuations plugin for Scala. The compiler is integrated into the wider ABS Tool Suite, available at http://tools.hats-project.eu/. We are currently formalizing the results of the paper in the proof assistant Agda.\n\n## Footnotes\n\n1. 1.\n\nIn ABS, different tasks originating from the same object may communicate with each other via fields of the object.\n\n## References\n\n1. Adya, A., Howell, J., Theimer, M., Bolosky, W.J., Douceur, J.R.: Cooperative task management without manual stack management. In: ATEC 2002: Proceedings of the General Track of the Annual Conference on USENIX Annual Technical Conference, pp. 289–302. USENIX (2002)Google Scholar\n2. Agha, G.: Actors: a model of concurrent computation in distributed systems. MIT Press (1986)Google Scholar\n3. de Boer, F.S., Clarke, D., Johnsen, E.B.: A complete guide to the future. In: De Nicola, R. (ed.) ESOP 2007. LNCS, vol. 4421, pp. 316–330. Springer, Heidelberg (2007)Google Scholar\n4. Caromel, D., Henrio, L., Serpette, B.P.: Asynchronous and deterministic objects. ACM SIGPLAN Notices - POPL 2004 39(1), 123–134 (2004)Google Scholar\n5. Danvy, O., Filinski, A.: Abstracting control. In: LFP 1990: Proceedings of the 1990 ACM Conference on LISP and Functional Programming, pp. 151–160. ACM (1990)Google Scholar\n6. Haynes, C.T., Friedman, D.P., Wand, M.: Continuations and coroutines. In: LFP 1984: Proceedings of the 1984 ACM Symposium on LISP and Functional Programming, pp. 293–298. ACM (1984)Google Scholar\n7. Johnsen, E.B., Hähnle, R., Schäfer, J., Schlatte, R., Steffen, M.: ABS: A core language for abstract behavioral specification. In: Aichernig, B.K., de Boer, F.S., Bonsangue, M.M. (eds.) FMCO2010. LNCS, vol. 6957, pp. 142–164. Springer, Heidelberg (2011)Google Scholar\n8. Johnsen, E.B., Owe, O., Yu, I.C.: Creol: A type-safe object-oriented model for distributed concurrent systems. Theoretical Computer Science 365(1-2), 23–66 (2006)Google Scholar\n9. Karmani, R.K., Shali, A., Agha, G.: Actor frameworks for the JVM platform: a comparative analysis. In: PPPJ 1909: Proceedings of the 7th International Conference on Principles and Practice of Programming in Java, pp. 11–20. ACM (2009)Google Scholar\n10. Schäfer, J., Poetzsch-Heffter, A.: JCoBox: Generalizing active objects to concurrent components. In: D’Hondt, T. (ed.) ECOOP 2010. LNCS, vol. 6183, pp. 275–299. Springer, Heidelberg (2010)Google Scholar\n11. Srinivasan, S., Mycroft, A.: Kilim: Isolation-typed actors for Java. In: Vitek, J. (ed.) ECOOP 2008. LNCS, vol. 5142, pp. 104–128. Springer, Heidelberg (2008)Google Scholar\n12. Wand, M.: Continuation-based multiprocessing. In: LFP 1980: Proceedings of the 1980 ACM Conference on LISP and Functional Programming, pp. 19–28. ACM (1980)Google Scholar" ]

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[ "# Fun with DAX – Tic Tac Toe\n\nTo follow in the spirit of some of my recent blogs, I thought I would have a look to see how feasible it might be to build a Tic Tac Toe game using just DAX and Power BI.  I get pretty close and will detail my approach here in this article.  For starters, here is a link to a playable “Publish to Web” version so you can try it out for yourself.\n\nPublish to web version\n\nPBIX and Data Files", null, "A caveat I would like to make early in the article is the game gets confused about 5% of the time, so you may notice the computer pieces jump to a completely different layout if you play it often enough.  If this happens, click the reset button in the top left corner and have another go.  The reason for this will become clear later in the article.\n\nOnce again, I’d like to give a big thanks to Mike Carlo and the team over at PowerBI.Tips for coming up with some fantastic images for the game.  If you see the layout of the game without images, you’ll agree the graphics improve the look and feel out of this world.\n\n## The Game Engine\n\nThe main challenge with this and any game using DAX in Power BI is how to keep of each player’s moves.  In this game, there are two players, you the user against the DAX engine.  The moves made by the end user are easy enough to track by combining slicers and bookmarks.  Keeping track of the moves by DAX is harder as there is no current way in DAX to store state, or to make a selection on an object as the output of a calculation.  Let’s first look at how I keep track of the moves made by the person playing the game.\n\nThe first thing I do is assign a numeric value to each square on the board as follows.  This is deliberately set in this curl pattern to make some adjustments later on much easier to make.", null, "Each square is assigned a physical table with a single column and only a couple of rows.  There are 9 of these tables that are used to keep track of the moves made human player of the game.  The physical table looks like this and is not related to any another table in the data model:", null, "Nine slicers are added to the game board with each slicer using one of the nine physical tables.   Nine bookmarks are then added to the PBIX File as follows.  The bookmark for Cell 1 is used to see the slicer for cell 1 to the number 1.", null, "A handy feature of bookmarks which I take full advantage of, is you can set individual bookmarks to only snapshot the “selected objects”.   So, for each of the nine bookmarks, a single slicer is set with a selection of 1 before the bookmark is Updated.  I use this to make sure the bookmark associated with each square on the playing board affects just the slicer tied to the same square.", null, "The “Reset” bookmark is set to snapshot “All visuals” with care being taken to make sure all the slicers on the canvas have no selection.  This provides a mechanism to reset the board to start again.\n\nWith the bookmarks being configured using “Selected visuals” instead of “All Visuals”, this allows bookmarks to be actioned in a way that accumulates moves for the human player.  This means if the bookmark that controls the top-left square is actioned, only that slicer is set to one.  Then if another bookmark on the board is actioned, say the centre square, then the slicer that belongs to the centre square is set to 1, while the slicer set earlier retains its state.\n\nFinally, nine buttons are added to the game board.  The format properties for each button are set so it appears invisible and then positioned over each square with the action set to the relevant bookmark, provides a way to capture the moves made in the correct order for the human player.\n\n## Binary Storage\n\nThe next thing to do is to compress all moves made by the human number down to a single value that represents each square played.  If the square has had a piece played by the human player, its slicer is set to 1, otherwise, it will be 0.  So in the example below, the human has made two moves.  The top left cell (1) along with the right cell of the middle row (8).  When these two values are added together I can represent this using the decimal value of 9 or a binary value of 000001001.", null, "Using this method, if the human player decides to place a piece in the center of the board (256), this now can be represented using the decimal number of 265 (256 + 8 + 1), which in binary form looks like 10001001.  Basically, each of the nine 1/0 bits stores if the human player has made a move in a cell.", null, "I use the following [Player 1 Positions] calculated measure to first determine the decimal (Base10) value by checking the state of all nine slicers.\n\n```Player 1 Positions =\nIF(SELECTEDVALUE('R1'[Value])=1,1,0) +\nIF(SELECTEDVALUE('R2'[Value])=1,2,0) +\nIF(SELECTEDVALUE('R3'[Value])=1,4,0) +\nIF(SELECTEDVALUE('R4'[Value])=1,8,0) +\nIF(SELECTEDVALUE('R5'[Value])=1,16,0) +\nIF(SELECTEDVALUE('R6'[Value])=1,32,0) +\nIF(SELECTEDVALUE('R7'[Value])=1,64,0) +\nIF(SELECTEDVALUE('R8'[Value])=1,128,0) +\nIF(SELECTEDVALUE('R9'[Value])=1,256,0)```\n\nThe’Binary Mapping’ table can be filtered down to a single row using the above decimal value as a filter to get access to the binary representation of the number if required.\n\n```Player 1 Positions Binary =\nMINX(\nFILTER(\n'Binary Mapping',\n'Binary Mapping'[Value]=[Player 1 Positions]\n),\n'Binary Mapping'[Binary2]\n)```\n\nThe next part is to have nine visuals to show the relevant piece. This is the only aspect of the PBIX file that doesn’t use native DAX.  I use an image viewer control from the marketplace to display an image stored in a physical table.   I will provide more detail on how the images were imported, stored, dynamically selected using a calculated measure to eventually display the piece on the board in my next blog.\n\nSo far, I have covered the mechanism used to allow the human player to make moves in the game.  Hopefully, this is pretty straightforward and shows creative usage of bookmarks, slicers and DAX calculations.\n\n## Computer Moves\n\nThe fun begins when adding logic to allow the DAX engine to play moves.  As mentioned earlier, DAX has no ability to make selections on tables.  Once the human user has made a move, this causes a selection to be made on a slicer which in turn triggers any measure used in a visual to be re-calculated.  There are nine measures used on the game board that determine game piece to display.    The human player peices are easy to manage, as these can be determined by referencing the [Player 1 Positions] calculated measure.  The next step is to look up a list of pre-played moves saved in a CSV data file that follows the following pattern.\n\nThere are three columns in total (and approximately 100 rows of pre-played moves).  The first column represents the binary mapping of the human players’ moves.  This is mapped to the board using the clockwise swirl pattern.  The fifth row has a value in the first column of 67 which in binary is 0 + 0 + 64 + 0 + 0 + 0 + 0 + 2 + 1  (001000011).", null, "When mapped to the gameboard mean the human player has played three pieces as follows :", null, "The second column in the CSV file determines the square last played by the human player.  In the fifth row, this value is a 7 which when mapped to the board using the clockwise swirl system represents the square in the lower right-hand side.  There is a separate slicer that tracks the last move made by each player.  This is to help provide some clarity on the order the pieces that have been played.  This is the weakness of my approach.  While I can tell that the human player has made three moves, and which of the last moves have been played, I can’t tell which order the top two pieces have been played.\n\nThe final column in the CSV file tells me where to place the computer pieces based on the information in the first two columns.  The value in the fifth row is 388.  In binary, this maps to 110000100 and therefore means I need to place three pieces computer pieces on the board in position 9, 8 and 3", null, "The challenge with DAX is there is no place to proactively store dynamic information, which removes from DAX any ability to provide logic to respond progressively to pieces as they are played.  The pre-played dataset is pretty good, especially with the addition of the middle column in the CSV file to control which was the last move made by the human player.   Before I added this, I was hitting ambiguous game-states more often.\n\n## Building the Pre-played game dataset\n\nSo with the game logic sorted, the challenge was to generate data for the moves.csv file that contains the instructions on how to place the computer pieces based on any given known state of the human played game.  I’m no data scientist and after some pretty basic maths, I decided there probably weren’t too many permutations on gameplay so I decided to build these by hand.  What I had in my favour was I could ‘cheat’ by re-using game play data by rotating and flipping.\n\nI knew I would allow the human player to make the first move each game, and there are realistically only three possible starting moves.  I would only write data to assume player 1 had started in either the top two right-hand squares and the centre square as highlighted.  Once I had generated each permutation of response for these opening moves, I would make three copies of the dataset with each dataset being a mirror of the base set only rotated 90°, 180° and 270°.  I did not need to generate copies if the opening move by the human player is in the centre square.", null, "My system of mapping binary positions to squares made rotating the dataset very easy.  For 90°, I could just grab two bits from the near the start of the number and move them to the end.\n\nSo in the following example, the 2nd and 3rd bits which are both 0’s are removed and placed at the end if you read left to right. The right-most bit is the center square so is always left alone.", null, "To rotate 180°, four bits are moved and for 270° 6 bits are moved.  The DAX I used to manage this is as follows:\n\nI start with the data contained in the moves.csv which I load into the Unrotated variable.  I then make multiple copies of the dataset but apply the relevant rotation rule before finally joining all the datasets back together in a UNION at the end.\n\n```Pre Played Games =\nVAR Rotated90Deg =\nSELECTCOLUMNS(\nFILTER(moves,[Player 1] < 256),\n\"P1 Rotated\",\nVAR StartVal = 'moves'[Player 1]\nVAR b = MINX(FILTER('Binary Mapping','Binary Mapping'[Value]= StartVal),'Binary Mapping'[Binary2])\nVAR CenterMove=MID(b,1,1)\nVAR BinaryShift=MID(b,2,2)\nVAR bFinal = CenterMove & MID(b,4,6) & BinaryShift\nRETURN MINX(FILTER('Binary Mapping','Binary Mapping'[Binary2] = bFinal),'Binary Mapping'[Value])\n,\n\"LM Rotated\",VAR x = 'moves'[Last Move] RETURN SWITCH(TRUE(),x<7,x+2,x<9,x-6,x),\n\n\"P2 Rotated\",\nVAR StartVal = 'moves'[Player 2]\nVAR b = MINX(FILTER('Binary Mapping','Binary Mapping'[Value]= StartVal),'Binary Mapping'[Binary2])\nVAR CenterMove=MID(b,1,1)\nVAR BinaryShift=MID(b,2,2)\nVAR bFinal = CenterMove & MID(b,4,6) & BinaryShift\nRETURN MINX(FILTER('Binary Mapping','Binary Mapping'[Binary2] = bFinal),'Binary Mapping'[Value])\n),\n\"P1 Player\",[P1 Rotated] ,\n\"Last Move\",[LM Rotated],\n\"P2 Player\",[P2 Rotated] ,\n\"X\",2\n)\n\nVAR Rotated180Deg =\nSELECTCOLUMNS(\nFILTER(moves,[Player 1] < 256),\n\"P1 Rotated\",\nVAR StartVal = 'moves'[Player 1]\nVAR b = MINX(FILTER('Binary Mapping','Binary Mapping'[Value]= StartVal),'Binary Mapping'[Binary2])\nVAR CenterMove=MID(b,1,1)\nVAR BinaryShift=MID(b,2,4)\nVAR bFinal = CenterMove & MID(b,6,4) & BinaryShift\nRETURN MINX(FILTER('Binary Mapping','Binary Mapping'[Binary2] = bFinal),'Binary Mapping'[Value])\n,\n\"LM Rotated\",VAR x = 'moves'[Last Move] RETURN SWITCH(TRUE(),x<5,x+4,x<9,x-4,x),\n\n\"P2 Rotated\",\nVAR StartVal = 'moves'[Player 2]\nVAR b = MINX(FILTER('Binary Mapping','Binary Mapping'[Value]= StartVal),'Binary Mapping'[Binary2])\nVAR CenterMove=MID(b,1,1)\nVAR BinaryShift=MID(b,2,4)\nVAR bFinal = CenterMove & MID(b,6,4) & BinaryShift\nRETURN MINX(FILTER('Binary Mapping','Binary Mapping'[Binary2] = bFinal),'Binary Mapping'[Value])\n) ,\n\"P1 Player\",[P1 Rotated] ,\n\"Last Move\",[LM Rotated],\n\"P2 Player\",[P2 Rotated],\n\"X\",3\n)\nVAR Rotated2700Deg =\nSELECTCOLUMNS(\nFILTER(moves,[Player 1] < 256),\n\"P1 Rotated\",\nVAR StartVal = 'moves'[Player 1]\nVAR b = MINX(FILTER('Binary Mapping','Binary Mapping'[Value]= StartVal),'Binary Mapping'[Binary2])\nVAR CenterMove=MID(b,1,1)\nVAR BinaryShift=MID(b,2,6)\nVAR bFinal = CenterMove & MID(b,8,2) & BinaryShift\nRETURN MINX(FILTER('Binary Mapping','Binary Mapping'[Binary2] = bFinal),'Binary Mapping'[Value])\n,\n\"LM Rotated\",VAR x = 'moves'[Last Move] RETURN SWITCH(TRUE(),x<3,x+6,x<9,x-2,x),\n\"P2 Rotated\",\nVAR StartVal = 'moves'[Player 2]\nVAR b = MINX(FILTER('Binary Mapping','Binary Mapping'[Value]= StartVal),'Binary Mapping'[Binary2])\nVAR CenterMove=MID(b,1,1)\nVAR BinaryShift=MID(b,2,6)\nVAR bFinal = CenterMove & MID(b,8,2) & BinaryShift\nRETURN MINX(FILTER('Binary Mapping','Binary Mapping'[Binary2] = bFinal),'Binary Mapping'[Value])\n) ,\n\"P1 Player\",[P1 Rotated] ,\n\"Last Move\",[LM Rotated],\n\"P2 Player\",[P2 Rotated],\n\"X\",4\n)\n\nVAR Flipped =\nSELECTCOLUMNS(\nFILTER(moves,[Player 1] >= 256),\n\"P1 Rotated\",\nVAR StartVal = 'moves'[Player 1]\nVAR b = MINX(FILTER('Binary Mapping','Binary Mapping'[Value]= StartVal),'Binary Mapping'[Binary2])\nVAR Bit1=MID(b,9,1)\nVAR Bit2=MID(b,8,1)\nVAR Bit3=MID(b,7,1)\nVAR Bit4=MID(b,6,1)\nVAR Bit5=MID(b,5,1)\nVAR Bit6=MID(b,4,1)\nVAR Bit7=MID(b,3,1)\nVAR Bit8=MID(b,2,1)\nVAR Bit9=MID(b,1,1)\nVAR bFinal= Bit9 & Bit2 & Bit3 & Bit4 & Bit5 & Bit6 & Bit7 & Bit8 & Bit1 // Swap bits 2 with 8, 3 with 7 and 4 with 6\nRETURN MINX(FILTER('Binary Mapping','Binary Mapping'[Binary2] = bFinal),'Binary Mapping'[Value])\n,\n\"LM Rotated\",\nVAR x = 'moves'[Last Move]\nRETURN\nSWITCH(\nTRUE(),\nx=4,6,\nx=3,7,\nx=2,8,\nx=6,4,\nx=7,3,\nx=8,2,\nx),\n\"P2 Rotated\",\nVAR StartVal = 'moves'[Player 2]\nVAR b = MINX(FILTER('Binary Mapping','Binary Mapping'[Value]= StartVal),'Binary Mapping'[Binary2])\nVAR Bit1=MID(b,9,1)\nVAR Bit2=MID(b,8,1)\nVAR Bit3=MID(b,7,1)\nVAR Bit4=MID(b,6,1)\nVAR Bit5=MID(b,5,1)\nVAR Bit6=MID(b,4,1)\nVAR Bit7=MID(b,3,1)\nVAR Bit8=MID(b,2,1)\nVAR Bit9=MID(b,1,1)\nVAR bFinal= Bit9 & Bit2 & Bit3 & Bit4 & Bit5 & Bit6 & Bit7 & Bit8 & Bit1 // Swap bits 2 with 8, 3 with 7 and 4 with 6\nRETURN MINX(FILTER('Binary Mapping','Binary Mapping'[Binary2] = bFinal),'Binary Mapping'[Value])\n) ,\n\"P1 Player\",[P1 Rotated] ,\n\"Last Move\",[LM Rotated],\n\"P2 Player\",[P2 Rotated],\n\"X\",5\n)\n\nRETURN\nUNION(\nUnrotated,Rotated90Deg,Rotated180Deg,Rotated2700Deg,Flipped)```\n\nThe calculation also includes code to generate a flipped set of the code based on a diagonal mirror from top left to bottom right.  In this case, I swap bits 8 and 2, 7 and 3, 4 and 6, to give an extra set of pre-played combinations.", null, "Once these have been applied, my 148 manually created states become 476 scenarios that can be used to place the computer peices depending on what the human player has done.  95% of the time, this plays out nicely and makes it look like the computer is responding to the human as pieces are played.  In reality, like me, DAX forgets things easily and computations can only use current selections and can’t look back to help guide any output.\n\nI quite like the simplicity of the bitwise approach to mapping – and it certainly made multiplying the game permutations an easier job.  It’s not perfect and I have made sure there are scenarios where the human can win the game.\n\n## Images\n\nThe images used for game pieces were stored as png files in a local folder (c:\\x).  I used the folder data source to import the files and converted the binary column to text.  I then strip out unused columns and prefix the converted text with the magic “data:image/png;base64, ” string, which seems to be enough to allow some Power BI Visuals to display images.  Full credit to this blog post for the original idea.\n\n```let\nSource = Folder.Files(\"c:\\x\"),\n#\"Changed Type\" = Table.TransformColumnTypes(Source,{{\"Content\", type text}}),\n#\"Removed Other Columns\" = Table.SelectColumns(#\"Changed Type\",{\"Content\", \"Name\"}),\n#\"Added Prefix\" = Table.TransformColumns(#\"Removed Other Columns\", {{\"Content\", each \"data:image/png;base64, \" & _, type text}}),\n#\"Extracted First Characters\" = Table.TransformColumns(#\"Added Prefix\", {{\"Name\", each Text.Start(_, 2), type text}}),\n#\"Inserted Last Characters\" = Table.AddColumn(#\"Extracted First Characters\", \"Last Characters\", each Text.End([Name], 1), type text),\n#\"Filtered Rows\" = Table.SelectRows(#\"Inserted Last Characters\", each ([Last Characters] = \"4\")),\n#\"Extracted First Characters1\" = Table.TransformColumns(#\"Filtered Rows\", {{\"Name\", each Text.Start(_, 1), type text}})\nin\n#\"Extracted First Characters1\"```\n\nThen with a little DAX magic, using disconnected tables and making 9 copies of the table of images imported using Power Query.  The tables are named P1 through P9 and each contains a calculated measure which is used as a visual filter to determine which, if any, image should be used.\n\n`P1 Filter = IF([M 1]=MIN('P1'[Name]),1,0)`\n\nThis part of the game was the only departure from using 100% native Power BI.  I needed to use a custom visual to display the images to get it to look the way I want.\n\nThere is a fair amount to take in, and I would love to see your comments.  I will probably convert this to a presentation that might be interesting enough to deliver in a webinar as part of the Power BI series.\n\nPhil is Microsoft Data Platform MVP and an experienced database and business intelligence (BI) professional with a deep knowledge of the Microsoft B.I. stack along with extensive knowledge of data warehouse (DW) methodologies and enterprise data modelling. He has 25+ years experience in this field and an active member of Power BI community.\n\n## 4 thoughts on “Fun with DAX – Tic Tac Toe”\n\n•", null, "Marc says:\n\nOops a little bug is introduced.\nIf I take the first step and click somewhere on the board, the computer takes the next step afterwards. But when I click on the same spot as the computer did, the bug is introduced. The computer stops playing and I will always win.\n\nBut beside of that respect for what you did! Nice job!\n\n•", null, "Clayton says:\n\nDoing things like this is frivolous, fun and necessary. What better way to push your creativity and push the limits of what is possible with the Power BI platform.\nDefinitely in the vein of the “BI Power Hour” presentations at SQL PASS in years past." ]

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[ "##", null, "帐号 自动登录 找回密码 密码 立即注册→加入我们\n 搜索 热搜: 下载 VB C 实现 编写\n\n# 【VFB】变量和数据类型（VFB教程2-3）\n\n51主题 642积分\n\nUID\n3260\n\n7\n\n12 点\n\n502 个\n\n1 次\n\n0 份\n\n22 小时\n\n2017-12-26", null, "发表于 2018-2-26 21:13:37 | 显示全部楼层 |阅读模式\n\n### 欢迎访问技术宅的结界，请注册或者登录吧。\n\nx\n\n[Visual Basic] 纯文本查看 复制代码\n'--------------------------------------------------------------------------------\nFunction FORM1_COMMAND1_BN_CLICKED ( _\nControlIndex As Long, _ ' 控件数组的索引\nhWndForm As HWnd, _ ' 窗体句柄\nhWndControl As HWnd, _ ' 控件句柄\nidButtonControl As Long _ ' 按钮的标识符\n) As Long\nDim FirstNumber As Integer\nDim Shared SecondNumber As Integer\n\nFirstNumber = 1\nSecondNumber = 2\n\nPrintConstants ()\nPrint FirstNumber, SecondNumber, ThirdNumber '这将打印1 2 0\nEnd Function\n'--------------------------------------------------------------------------------\nSub PrintConstants ()\nDim ThirdNumber As Integer\nThirdNumber = 3\nPrint FirstNumber, SecondNumber, ThirdNumber '这将打印0 2 3\nEnd Sub\n\n[Visual Basic] 纯文本查看 复制代码\nConst FirstNumber = 1\nConst SecondNumber = 2\nConst FirstString = \"第一个字符串\"\n'--------------------------------------------------------------------------------\nFunction FORM1_COMMAND1_BN_CLICKED ( _\nControlIndex As Long, _ ' 控件数组的索引\nhWndForm As HWnd, _ ' 窗体句柄\nhWndControl As HWnd, _ ' 控件句柄\nidButtonControl As Long _ ' 按钮的标识符\n) As Long\nPrint FirstNumber, SecondNumber '这将打印1 2\nPrint FirstString '这将打印第一个字符串。\nPrintConstants ()\nEnd Function\n'--------------------------------------------------------------------------------\nSub PrintConstants ()\nPrint FirstNumber, SecondNumber '这也将打印1 2\nPrint FirstString '这也将打印第一个字符串。\nEnd Sub\n\n[Visual Basic] 纯文本查看 复制代码\n' Create an array of 3 elements all having the value zero (0.0f).\nDim array(1 To 3) As Single\n\n' Assign a value to the first element.\narray(1) = 1.2\n\n' Output the values of all the elements (\"1.2 0 0\").\nFor position As Integer = 1 To 3\nPrint array(position)\nNext\n\n[Visual Basic] 纯文本查看 复制代码\n' Declares and initializes an array of four integer elements.\nDim array(3) As Integer = { 10, 20, 30, 40 }\n\n' Outputs all of the element values (\" 10 20 30 40\").\nFor position As Integer = LBound(array) To UBound(array)\nPrint array(position) ;\nNext\n\n[Visual Basic] 纯文本查看 复制代码\n' Creates a fixed-length array that holds 5 single elements.\nConst totalSingles = 5\nDim flarray(1 To totalSingles) As Single\n\n' Creates an empty variable-length array that holds integer values.\nDim vlarray() As Integer\n\n' Resizes the array to 10 elements.\nReDim vlarray(1 To 10) As Integer\n\n[Visual Basic] 纯文本查看 复制代码\n' Take Care while initializing multi-dimensional array\nDim As Integer multidim(1 To 2,1 To 5) = {{0,0,0,0,0},{0,0,0,0,0}}\n\n[Visual Basic] 纯文本查看 复制代码\n'' Defines a one-dimensional fixed-length array of type INTEGER having automatic storage.\nDim arrayOfIntegers(69) As Integer\n\n'' Defines a one-dimensional fixed-length array of type SHORT having static storage.\nStatic arrayOfShorts(420) As Short\n\n[Visual Basic] 纯文本查看 复制代码\nDim a(1) As Integer '' 1-dimensional, 2 elements (0 and 1)\nDim b(0 To 1) As Integer '' 1-dimensional, 2 elements (0 and 1)\nDim c(5 To 10) As Integer '' 1-dimensional, 5 elements (5, 6, 7, 8, 9 and 10)\n\nDim d(1 To 2, 1 To 2) As Integer '' 2-dimensional, 4 elements: (1,1), (1,2), (2,1), (2,2)\nDim e(255, 255, 255, 255) As Integer '' 4-dimensional, 256 * 256 * 256 * 256 elements\n\n[Visual Basic] 纯文本查看 复制代码\nConst myLowerBound = -5\nConst myUpperBound = 10\n\n'' Declares a one-dimensional fixed-length array, holding myUpperBound - myLowerBound + 1 String objects.\nDim arrayOfStrings(myLowerBound To myUpperBound) As String\n\n'' Declares a one-dimensional fixed-length array of bytes,\n'' big enough to hold an INTEGER.\nDim arrayOfBytes(0 To SizeOf(Integer) - 1) As Byte\n\n[Visual Basic] 纯文本查看 复制代码\n'' Declares a one-dimensional variable-length array of integers, with initially 2 elements (0 and 1)\nReDim a(0 To 1) As Integer\n\n'' Declares a 1-dimensional variable-length array without initial bounds.\n'' It must be resized using Redim before it can be used for the first time.\nDim b(Any) As Integer\n\n'' Same, but 2-dimensional\nDim c(Any, Any) As Integer\n\nDim myLowerBound As Integer = -5\nDim myUpperBound As Integer = 10\n\n'' Declares a 1-dimensional variable-length array by specifying variable (non-constant) boundaries.\n'' The array will have myUpperBound - myLowerBound + 1 elements.\nDim d(myLowerBound To myUpperBound) As Integer\n\n'' Declares a variable-length array whose amount of dimensions will be determined\n'' by the first Redim or array access found. The array has no initial bounds and must\n'' be resized using Redim before it can be used for the first time.\nDim e() As Integer\n\n[Visual Basic] 纯文本查看 复制代码\n'' Define an empty 1-dimensional variable-length array of SINGLE elements...\nDim array(Any) As Single\n\n'' Resize the array to hold 10 SINGLE elements...\nReDim array(0 To 9) As Single\n\n'' The data type may be omitted when resizing:\nReDim array(10 To 19)\n\n[Visual Basic] 纯文本查看 复制代码\nIndex Data\n1 5\n2 2\n3 6\n4 5\n5 9\n6 1\n7 0\n8 4\n9 5\n10 7\n\n[Visual Basic] 纯文本查看 复制代码\nPrint myArray(5)\n\n9\n\n[Visual Basic] 纯文本查看 复制代码\nmyArray(3) = 0\n\n[Visual Basic] 纯文本查看 复制代码\nPrint myArray(3)\n\n0\n\n[Visual Basic] 纯文本查看 复制代码\n Dim a As Integer\nFor a = 1 To 10\nmyArray(a) = 0\nNext a\n\n[Visual Basic] 纯文本查看 复制代码\n Dim Index As Integer\nDim Value As Integer\nindex = Int(Rnd(1) * 10) + 1 'This line will simply return a random value between 1 and 10\nValue = Int(Rnd(1) * 10) + 1 'This line will do the same\nmyArray(index) = Value\n\n[Visual Basic] 纯文本查看 复制代码\nDim Numbers(1 To 10) As Integer\nDim Shared OtherNumbers(1 To 10) As Integer\nDim a As Integer\n\nNumbers(1) = 1\nNumbers(2) = 2\nOtherNumbers(1) = 3\nOtherNumbers(2) = 4\n\nPrintArray ()\n\nFor a = 1 To 10\nPrint Numbers(a)\nNext a\n\nPrint OtherNumbers(1)\nPrint OtherNumbers(2)\nPrint OtherNumbers(3)\nPrint OtherNumbers(4)\nPrint OtherNumbers(5)\nPrint OtherNumbers(6)\nPrint OtherNumbers(7)\nPrint OtherNumbers(8)\nPrint OtherNumbers(9)\nPrint OtherNumbers(10)\n\nSub PrintArray ()\nDim a As Integer\nFor a = 1 To 10\nPrint otherNumbers(a)\nNext a\nEnd Sub\n\nByte和UByte\n\nShort和UShort\n\nLong和Ulong\n\nInteger和UInteger\n\nLongInt和ULongInt\n\nSingle\n\nDouble\n\nConst\n\nPointer和Ptr\n\nUnsigned\n\nString\n\nZString\n\nWString\n\nObject\n\n 类型 大小在位 格式 最小值 最大值 字面后缀 SIG。数字 BYTE 8 有符号整数 -128 +127 2+ UBYTE 8 无符号整数 0 +255 2+ SHORT 16 有符号整数 -32768 +32767 4+ USHORT 16 无符号整数 0 65535 4+ LONG 32 有符号整数 -2147483648 +2147483647 &, l 9+ ULONG 32 无符号整数 0 4294967295 ul 9+ INTEGER 32/64 ［*］ 有符号整数 ［*］ ［*］ % ［*］ UINTEGER 32/64 ［*］ 无符号整数 ［*］ ［*］ u ［*］ LONGINT 64 有符号整数 -9 223 372 036 854 775 808 +9 223 372 036 854 775 807 ll 18+ ULONGINT 64 无符号整数 0 +18 446 744 073 709 551 615 ULL 19+ SINGLE 32 浮点 ［**］+/-1.401 298 E-45 ［**］+/-3.402 823 E+38 !, f 6+ DOUBLE 64 浮点 ［**］+/-4.940 656 458 412 465 E-324 ［**］+/-1.797 693 134 862 316 E+308 #, d 15+\n\n［*］ 整数和UInteger数据类型随平台而异，与指针的大小相匹配。\n［**］ 浮点类型Single和Double的最小值和最大值分别为最接近零的值，最接近正负无穷大的值。\n\n 类型 字符大小（字节） 最小尺寸（以字符） 最大尺寸（以字符） 字面后缀 string 1 0 ［**］+2147483647 \\$ zstring 1 0 ［**］+2147483647 [N/A] WSTRING ［*］ ［*］0 [*,**]+2147483647 [N/A]\n\n［*］ Unicode或“wide”，字符大小和可用性随平台而异。\n［**］ 所有运行时库字符串过程都会获取大小和位置的整数值。 实际的最大尺寸将随存储位置和/或平台而变化（较小）。\n\n 最大下标范围 每个维度的最大元素 最小/最大尺寸 最大大小（以字节为单位） ［*］[-2147483648, +2147483647] ［*］+2147483647 1/9 ［*］+2147483647\n\n［*］ 所有运行时库数组过程都会为下标和索引生成整数值。 实际限制将随维度数量，元素大小，存储位置和/或平台而变化（较小）。", null, "本版积分规则 回帖并转播 回帖后跳转到最后一页", null, "|申请友链||Archiver|手机版|小黑屋|技术宅的结界 ( 滇ICP备16008837号 )|网站地图\n\nGMT+8, 2020-12-3 05:42 , Processed in 0.095023 second(s), 32 queries , Gzip On." ]

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[ "# Question 1 Your finance text book sold 53,250 copies in its first year. The publishing company expects the sales to grow at a rate of\n\nQuestion 1 Your finance text book sold 53,250 copies in its first year. The publishing company expects the sales to grow at a rate of 20 percent for the next three years, and by 10 percent in the fourth year. Calculate the total number of copies that the publisher expects to sell in year 3 and 4. (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your final answers to the nearest whole number.) Find the present value of \\$3,500 under each of the following rates and periods. (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your final answer to the nearest penny.) a. 8.9 percent compounded monthly for five years. Present value \\$ b. 6.6 percent compounded quarterly for eight years. Present value \\$ c. 4.3 percent compounded daily for four years. Present value \\$ d. 5.7 percent compounded continuously for three years. Present value \\$ Question 3 Trigen Corp. management will invest cash flows of \\$331,000, \\$616,450, \\$212,775, \\$818,400, \\$1,239,644, and \\$1,617,848 in research and development over the next six years. If the appropriate interest rate is 6.75 percent, what is the future value of these investment cash flows six years from today? (Round answer to 2 decimal places, e.g. 15.25.) Question 4 You wrote a piece of software that does a better job of allowing computers to network than any other program designed for this purpose. A large networking company wants to incorporate your software into their systems and is offering to pay you \\$500,000 today, plus \\$500,000 at the end of each of the following six years for permission to do this. If the appropriate interest rate is 6 percent, what is the present value of the cash flow stream that the company is offering you? (Round answer to the nearest whole dollar, e.g. 5,275.) Question 5 Barbara is considering investing in a stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below, find Probability Return ________________________________________ Boom 0.1 25.00% Good 0.4 15.00% Level 0.3 10.00% Slump 0.2 -5.00% Question 6 Trevor Price bought 10-year bonds issued by Harvest Foods five years ago for \\$936.05. The bonds make semiannual coupon payments at a rate of 8.4 percent. If the current price of the bonds is \\$1,048.77, what is the yield that Trevor would earn by selling the bonds today? (Round intermediate calculations to 4 decimal places, e.g. 1.2514 and final answer to 2 decimal places, e.g. 15.25%.) Effective annual yield % Question 7 The First Bank of Ellicott City has issued perpetual preferred stock with a \\$100 par value. The bank pays a quarterly dividend of \\$1.65 on this stock. What is the current price of this preferred stock given a required rate of return of 11.6 percent? (Round answer to 2 decimal places, e.g. 15.25.) Current price" ]

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[ "", null, "", null, "", null, "Chapter 3.R, Problem 38E\n\nChapter\nSection\nTextbook Problem\n\n# Find two positive integers such that the sum of the first number and four times the second number is 1000 and the product of the numbers is as large as possible.\n\nTo determine\n\nTo find:\n\nTwo positive integers such that the sum of the first number and four times the second number is 1000 and product of the numbers is as large as possible.\n\nExplanation\n\n1) Concept:\n\nWe apply the second derivative test and critical numbers to find the two positive integers\n\nSecond derivative test:\n\nSuppose f'' is continuous near c\n\nIf f'c=0 and f''c>0 then f  has local minimum at c\n\nIf f'c=0 and f''c<0 then f  has local maximum at c\n\nCritical number:\n\nA critical number of a function f   is a number c in the domain of f  such that either  f'c=0 or f'c does not exist\n\n2) Given:\n\nConditions on integers:\n\nSum of the first number and four times the second number is 1000 and product of the numbers is as large as possible.\n\n3) Calculation:\n\nLet x and y be two integers, then by the given condition\n\nx+4y=1000 …………….. (1)\n\nFrom the above equation, x=1000-4y\n\nAlso, from another condition, the product of integers is as large as possible, so the equation becomes\n\nP=xy  ……………(2)\n\nSubstitute, x=1000-4y in the above equation.\n\nTherefore\n\nP(y)=1000-4yy  where y=0 y 250\n\nSimplify the right side of the equation,\n\nP(y)=1000y-4y2\n\nNow maximize the function P(y)\n\nDifferentiate P(y) with respect to y\n\n### Still sussing out bartleby?\n\nCheck out a sample textbook solution.\n\nSee a sample solution\n\n#### The Solution to Your Study Problems\n\nBartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!\n\nGet Started\n\n#### In Exercises 2336, find the domain of the function. 32. f(x)=1x2+x2\n\nApplied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach\n\n#### Evaluate the definite integrals in Problems 1-32.\n\nMathematical Applications for the Management, Life, and Social Sciences\n\n#### Which is the largest? a) f(a) b) f(b) c) f(c) d) cannot tell from information given\n\nStudy Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th", null, "" ]

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[ "# reconstruct_points_stereo (Operator)\n\n## Name\n\n`reconstruct_points_stereo` — Reconstruct 3D points from calibrated multi-view stereo images.\n\n## Signature\n\n`reconstruct_points_stereo( : : StereoModelID, Row, Column, CovIP, CameraIdx, PointIdx : X, Y, Z, CovWP, PointIdxOut)`\n\n## Description\n\nThe operator `reconstruct_points_stereo` reconstructs 3D points from point correspondences found in the images of a calibrated multi-view stereo setup. The calibration information for the images is provided in the camera setup model that is associated with the stereo model `StereoModelID` during its creation (see `create_stereo_model`). Note that the stereo model type must be 'points_3d', otherwise the operator will return an error.\n\nThe point correspondences must be passed in the parameters `Row`, `Column`, `CameraIdx`, and `PointIdx` in form of tuples of the same length. Each set `(Row[I],Column[I],CameraIdx[I],PointIdx[I])` represents the image coordinates (`Row`, `Column`) of the 3D point (`PointIdx`) in the image of a certain camera (`CameraIdx`).\n\nThe reconstructed 3D point coordinates are returned in the tuples `X`, `Y`, and `Z`, relative to the coordinate system of the camera setup model (see `create_camera_setup_model`). The tuple `PointIdxOut` contains the corresponding point indices.\n\nThe reconstruction algorithm works as follows: First, it identifies point correspondences for a given 3D point by collecting all sets with the same `PointIdx`. Then, it uses the `Row`, `Column`, and `CameraIdx` information from the collected sets to project lines of sight from each camera through the corresponding image point `[Row,Column]`. If there are at least 2 lines of sight for the point `PointIdx`, they are intersected and the result is stored as the set `(X[J],Y[J],Z[J],PointIdxOut[J])`. The intersection is performed with a least-squares algorithm, without taking into account potentially invalid lines of sight (e.g., if an image point was falsely specified as corresponding to a certain 3D point).\n\nTo compute the covariance matrices for the reconstructed 3D points, statistical information about the extracted image coordinates, i.e., the covariance matrices of the image points (see , e.g., `points_foerstner`) are needed as input and must be passed in the parameter `CovIP`. Otherwise, if no covariance matrices for the 3D points are needed or no covariance matrices for the image points are available, an empty tuple can be passed in `CovIP`. Then no covariance matrix for the reconstructed 3D points is computed.\n\nThe covariance matrix of an image point is:\n\nThe covariance matrices are symmetric `2x2` matrices, whose entries in the main diagonal represent the variances of the image point in row-direction and column-direction, respectively. For each image point, a covariance matrix must be passed in `CovIP` in form of a tuple with 4 elements:\n\nThus, `|CovIP|=4*|Row|` and `CovIP[I*4:I*4+3]` is the covariance matrix for the `I`-th image point.\n\nThe computed covariance matrix for a successfully reconstructed 3D point is represented by a symmetric `3x3` matrix:\n\nThe diagonal entries represent the variances of the reconstructed 3D point in x-, y-, and z-direction. The computed matrices are returned in the parameter `CovWP` in form of tuples each with 9 elements:\n\nThus, `|CovWP|=9*|X|` and `CovWP[J*9:J*9+8]` is the covariance matrix for the `J`-th 3D point. Note that if the camera setup associated with the stereo model contains the covariance matrices for the camera parameters, these covariance matrices are considered in the computation of `CovWP` too.\n\nIf the stereo model has a valid bounding box set (see `set_stereo_model_param`), the resulting points are clipped to this bounding box, i.e., points outside it are not returned. If the bounding box associated with the stereo model is invalid, it is ignored and all points that could be reconstructed are returned.\n\n## Execution Information\n\n• Multithreading type: reentrant (runs in parallel with non-exclusive operators).\n• Processed without parallelization.\n\n## Parameters\n\n`StereoModelID` (input_control)  stereo_model `→` (handle)\n\nHandle of the stereo model.\n\n`Row` (input_control)  number(-array) `→` (real / integer)\n\nRow coordinates of the detected points.\n\n`Column` (input_control)  number(-array) `→` (real / integer)\n\nColumn coordinates of the detected points.\n\n`CovIP` (input_control)  number-array `→` (real / integer)\n\nCovariance matrices of the detected points.\n\nDefault value: []\n\n`CameraIdx` (input_control)  number `→` (integer)\n\nIndices of the observing cameras.\n\nSuggested values: 0, 1, 2\n\n`PointIdx` (input_control)  number `→` (integer)\n\nIndices of the observed world points.\n\nSuggested values: 0, 1, 2\n\n`X` (output_control)  real(-array) `→` (real)\n\nX coordinates of the reconstructed 3D points.\n\n`Y` (output_control)  number(-array) `→` (real)\n\nY coordinates of the reconstructed 3D points.\n\n`Z` (output_control)  number(-array) `→` (real)\n\nZ coordinates of the reconstructed 3D points.\n\n`CovWP` (output_control)  number(-array) `→` (real)\n\nCovariance matrices of the reconstructed 3D points.\n\n`PointIdxOut` (output_control)  number(-array) `→` (integer)\n\nIndices of the reconstructed 3D points.\n\n## Alternatives\n\n`reconstruct_surface_stereo`, `intersect_lines_of_sight`\n\n3D Metrology" ]

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[ "# GandaniKristhel", null, "```The\nPigeonhole\nPrinciple\nThe Pigeonhole Principle\nSuppose that a flock of 20 pigeons flies into a set of 19\npigeonholes to roost. Because there are 20 pigeons but only 19\npigeonholes, at least one of these 19 pigeonholes must have at least two\npigeons in it. To see why this is true, note that if each pigeonhole had at\nmost one pigeon in it, at most 19 pigeons, one per hole, could be\naccommodated. This illustrates a general principle called the\npigeonhole principle, which states that if there are more pigeons than\npigeonholes, then there must be at least one pigeonhole with at least\ntwo pigeons in it.\nThe Pigeonhole Principle\nTheorem\nIf “A” is the average number of pigeons per hole, where A is not an\ninteger then\n• At least one pigeonhole contains ceil[A] (smallest integer greater\nthan or equal to A) pigeons\n• Remaining pigeonholes contains at most floor[A] (largest integer\nless than or equal to A) pigeons\nThe Pigeonhole Principle\nTheorem\nor we can say as, if n + 1 objects are put into n boxes, then at least\none box contains two or more objects.\nThe abstract formulation of the principle: Let X and Y be finite sets\nand let f : A → B be a function.\n• If X has more elements than Y, then f is not one-to-one.\n• If X and Y have the same number of elements and f is onto, then f\nis one-to-one.\n• If X and Y have the same number of elements and f is one-to-one,\nthen f is onto.\nThe Pigeonhole Principle\nPigeonhole principle is one of the simplest but most useful ideas in\nmathematics. Here are some examples:\n1) If (kn + 1) pigeons are kept in n pigeonholes where k is a positive\ninteger, what is the average no. of pigeons per pigeonhole?\nSolution:\nAverage number of pigeons per hole = (kn + 1)/n = k + 1/n\nTherefore, there will be at least one pigeonhole which will contain\nat least (k + 1) pigeons i.e., ceil[k +1/n] and remaining will contain\nat most k i.e., floor[k + 1/n] pigeons.\ni.e., the minimum number of pigeons required to ensure that at least\none pigeonhole contains (k + 1) pigeons is (kn + 1).\nThe Pigeonhole Principle\n2) A bag contains 10 red marbles, 10 green marbles, and 10 blue marbles. What is\nthe minimum no. of marbles you have to choose randomly from the bag to\nensure that we get 4 marbles of same color?\nSolution: Apply pigeonhole principle.\nNo. of colors (pigeonholes) n = 3\nNo. of marbles (pigeons) k + 1 = 4 → k = 3\nTherefore, the minimum no. of marbles required = kn + 1\nBy simplifying we get kn + 1 = 10.\ni.e., 3 red + 3 green + 3 blue + 1(red or green or blue) = 10\nThe Pigeonhole Principle\nPigeonhole principle strong form –\nTheorem\nLet q1, q2, . . . , qn be positive integers. If q1+ q2+ . . . + qn – n + 1\nobjects are put into n boxes, then either the 1st box contains at least\nq1 objects, or the 2nd box contains at least q2 objects, . . . , the nth box\ncontains at least qn objects.\nThe Pigeonhole Principle\nExample. In a computer science department, a student club can be\nformed with either 10 members from first year or 8 members from\nsecond year or 6 from third year or 4 from final year. What is the\nminimum no. of students we have to choose randomly from\ndepartment to ensure that a student club is formed?\nSolution:\nWe can directly apply from the above formula where,\nq1 = 10, q2 = 8, q3 = 6, q4 = 4 and n = 4\nTherefore, the minimum number of students required to ensure\ndepartment club to be formed is\n10 + 8 + 6 + 4 – 4 + 1 = 25.\nThe Pigeonhole Principle\nGeneralized Form of Pigeonhole Principle\nIf n pigeonholes are occupied by kn + 1 or more pigeons, where k\nis a positive integer, then at least one pigeonhole is occupied by\nk + 1 or more pigeons.\nThe Pigeonhole Principle\nExample. Find the minimum number of students in a class to be sure\nthat three of them are born in the same month.\nSolution:\nHere the n = 12 months are the pigeonholes, and k + 1 = 3 so k = 2.\nHence among any kn + 1 = 25 students (pigeons), three of them are\nborn in the same month.\nFactorial Function\nThe product of the positive integers from 1 to n inclusive is\ndenoted by n!, read “n factorial.” Namely:\nn! = 1・2・3・. . .・(n − 2)(n − 1)n = n(n − 1)(n − 2)・. . .・3・2・1\nAccordingly, 1! = 1 and n! = n(n − l)!.\nIt is also convenient to define 0! = 1.\nFactorial Function\nExample.\na) 3! = 3・2・1 = 6,\n4! = 4・3・2・1 = 24,\n5! = 5・4! = 5(24) = 120.\nb)\nand, more generally,\nc) For large n, one uses Stirling’s approximation (where e = 2.7128...):\nBinomial Coefficients\n𝑛\nThe symbol\n, read “nCr” or “n Choose r,” where r and n are\n𝑟\npositive integers with r ≤ n, is defined as\nfollows:\n𝑛 𝑛 − 1 ... 𝑛 −𝑟 + 1\n𝑛\n=\n𝑟\n𝑟 𝑟 − 1 ...3 ⋅ 2 ⋅ 1\n𝑜𝑟\n𝑛!\n𝑛\n=\n𝑟\n𝑟! 𝑛 − 𝑟 !\nNote that n − (n − r) = r. This yields the following important relation.\nBinomial Coefficients\n𝑛\n𝑛\n=\nLemma\nor equivalently,\n𝑛−𝑟\n𝑟\n𝑛\n𝑛\n=\n𝑎\n𝑏\nwhere a + b = n.\nMotivated by that fact that we defined 0! = 1, we define:\nBinomial Coefficients\nExample.\nExample.\nExample.\nBinomial Coefficients\nExample. Suppose we want to compute\n.\nThere will be 7 factors in both the numerator and the denominator.\nHowever, 10 − 7 = 3. Thus, we use Lemma 5.1 to compute:\nBinomial Coefficients &amp; Pascal’s Triangle\nThe numbers\nare called binomial coefficients, since they appear\nas the coefficients in the expansion of (a + b)n. Specifically:\nTheorem (Binomial Theorem):\nThe coefficients of the successive powers of a + b can be arranged\nin a triangular array of numbers, called Pascal’s triangle. The numbers\nin Pascal’s triangle have the following interesting properties:\nBinomial Coefficients &amp; Pascal’s Triangle\nThe numbers in Pascal’s triangle have the following interesting properties:\n(i) The first and last number in each row is 1.\n(ii) Every other number can be obtained by adding the two numbers appearing above it.\nFor example:\n10 = 4 + 6, 15 = 5 + 10, 20 = 10 + 10.\nSince these numbers are binomial coefficients, we state the above property formally.\nBinomial Coefficients &amp; Pascal’s Triangle\nTheorem\nBinomial Coefficients &amp; Pascal’s Triangle\nExample. Compute: a) 4!, 5!;\nb) 6!, 7!, 8!, 9!;\nc) 50!\nSolution.\na) 4! = 4・3・2・1 = 24\n5! = 5・4・3・2・1 = 5(24) = 120.\nb) Now use (n + 1)! = (n + 1)n!:\n6! = 6(5!) = 6(120) = 720,\n8! = 8(7!) = 8(5040) = 40 320,\n7! = 7(6!) = 7(720) = 5 040, 9! = 9(8!) = 9(40 320) = 362 880.\nc) Since n is very large, we use Sterling’s approximation:\n(where e ≈ 2.718). Thus:\nEvaluating N using a calculator, we get N = 3.04 &times; 1064 (which has 65 digits).\n```" ]

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[ "# pidstd2\n\nCreate 2-DOF PID controller in standard form, convert to standard-form 2-DOF PID controller\n\n## Syntax\n\n```C2 = pidstd2(Kp,Ti,Td,N,b,c) C2 = pidstd2(Kp,Ti,Td,N,b,c,Ts) C2 = pidstd2(sys) C2 = pid2(___,Name,Value) ```\n\n## Description\n\n`pid2` controller objects represent two-degree-of-freedom (2-DOF) PID controllers in parallel form. Use `pid2` either to create a `pid2` controller object from known coefficients or to convert a dynamic system model to a `pid2` object.\n\nTwo-degree-of-freedom (2-DOF) PID controllers include setpoint weighting on the proportional and derivative terms. A 2-DOF PID controller is capable of fast disturbance rejection without significant increase of overshoot in setpoint tracking. 2-DOF PID controllers are also useful to mitigate the influence of changes in the reference signal on the control signal. The following illustration shows a typical control architecture using a 2-DOF PID controller.", null, "`C2 = pidstd2(Kp,Ti,Td,N,b,c)` creates a continuous-time 2-DOF PID controller with proportional gain `Kp`, integrator and derivative time constants `Ti`, and `Td`, and derivative filter divisor `N`. The controller also has setpoint weighting `b` on the proportional term, and setpoint weighting `c` on the derivative term. The relationship between the 2-DOF controller’s output (u) and its two inputs (r and y) is given by:\n\n`$u={K}_{p}\\left[\\left(br-y\\right)+\\frac{1}{{T}_{i}s}\\left(r-y\\right)+\\frac{{T}_{d}s}{\\frac{{T}_{d}}{N}s+1}\\left(cr-y\\right)\\right].$`\n\nThis representation is in standard form. If all of the coefficients are real-valued, then the resulting `C2` is a `pidstd2` controller object. If one or more of these coefficients is tunable (`realp` or `genmat`), then `C2` is a tunable generalized state-space (`genss`) model object.\n\n`C2 = pidstd2(Kp,Ti,Td,N,b,c,Ts)` creates a discrete-time 2-DOF PID controller with sample time `Ts`. The relationship between the controller’s output and inputs is given by:\n\n`$u={K}_{p}\\left[\\left(br-y\\right)+\\frac{1}{{T}_{i}}IF\\left(z\\right)\\left(r-y\\right)+\\frac{{T}_{d}}{\\frac{{T}_{d}}{N}+DF\\left(z\\right)}\\left(cr-y\\right)\\right].$`\n\nIF(z) and DF(z) are the discrete integrator formulas for the integrator and derivative filter. By default,\n\n`$IF\\left(z\\right)=DF\\left(z\\right)=\\frac{{T}_{s}}{z-1}.$`\n\nTo choose different discrete integrator formulas, use the `IFormula` and `DFormula` properties. (See Properties for more information). If `DFormula` = `'ForwardEuler'` (the default value) and `N` ≠ `Inf`, then `Ts`, `Td`, and `N` must satisfy `Td/N > Ts/2`. This requirement ensures a stable derivative filter pole.\n\n`C2 = pidstd2(sys)` converts the dynamic system `sys` to a standard form `pidstd2` controller object.\n\n`C2 = pid2(___,Name,Value)` specifies additional properties as comma-separated pairs of `Name,Value` arguments.\n\n## Input Arguments\n\n `Kp` Proportional gain. `Kp` can be: A real and finite value.An array of real and finite values.A tunable parameter (`realp`) or generalized matrix (`genmat`).A tunable surface for gain-scheduled tuning, created using `tunableSurface`. Default: 1 `Ti` Integrator time. `Ti` can be: A real and positive value.An array of real and positive values.A tunable parameter (`realp`) or generalized matrix (`genmat`).A tunable surface for gain-scheduled tuning, created using `tunableSurface`. When `Ti` = `Inf`, the controller has no integral action. Default: `Inf` `Td` Derivative time. `Td` can be: A real, finite, and nonnegative value.An array of real, finite, and nonnegative values.A tunable parameter (`realp`) or generalized matrix (`genmat`).A tunable surface for gain-scheduled tuning, created using `tunableSurface`. When `Td` = 0, the controller has no derivative action. Default: 0 `N` Derivative filter divisor. `N` can be: A real and positive value.An array of real and positive values.A tunable parameter (`realp`) or generalized matrix (`genmat`).A tunable surface for gain-scheduled tuning, created using `tunableSurface`. When `N` = `Inf`, the controller has no filter on the derivative action. Default: `Inf` `b` Setpoint weighting on proportional term. `b` can be: A real, nonnegative, and finite value.An array of real, nonnegative, finite values.A tunable parameter (`realp`) or generalized matrix (`genmat`).A tunable surface for gain-scheduled tuning, created using `tunableSurface`. When `b` = 0, changes in setpoint do not feed directly into the proportional term. Default: 1 `c` Setpoint weighting on derivative term. `c` can be: A real, nonnegative, and finite value.An array of real, nonnegative, finite values.A tunable parameter (`realp`) or generalized matrix (`genmat`).A tunable surface for gain-scheduled tuning, created using `tunableSurface`. When `c` = 0, changes in setpoint do not feed directly into the derivative term. Default: 1 `Ts` Sample time. To create a discrete-time `pidstd2` controller, provide a positive real value (`Ts > 0`).`pidstd2` does not support discrete-time controller with undetermined sample time (`Ts = -1`). `Ts` must be a scalar value. In an array of `pidstd2` controllers, each controller must have the same `Ts`. Default: 0 (continuous time) `sys` SISO dynamic system to convert to standard `pidstd2` form. `sys` be a two-input, one-output system. `sys` must represent a valid 2-DOF controller that can be written in standard form with `Ti` > 0, `Td` ≥ 0, and `N` > 0. `sys` can also be an array of SISO dynamic systems.\n\n### Name-Value Arguments\n\nSpecify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.\n\nUse `Name,Value` syntax to set the numerical integration formulas `IFormula` and `DFormula` of a discrete-time `pidstd2` controller, or to set other object properties such as `InputName` and `OutputName`. For information about available properties of `pidstd2` controller objects, see Properties.\n\n## Output Arguments\n\n `C2` 2-DOF PID controller, returned as a `pidstd2` controller object, an array of `pidstd2` controller objects, a `genss` object, or a `genss` array. If all the coefficients have scalar numeric values, then `C2` is a `pidstd2` controller object. If one or more coefficients is a numeric array, `C2` is an array of `pidstd2` controller objects. The controller type (such as PI, PID, or PDF) depends upon the values of the gains. For example, when `Td` = 0, but `Kp` and `Ti` are nonzero and finite, `C2` is a PI controller. If one or more coefficients is a tunable parameter (`realp`), generalized matrix (`genmat`), or tunable gain surface (`tunableSurface`), then `C2` is a generalized state-space model (`genss`).\n\n## Properties\n\n `b, c` Setpoint weights on the proportional and derivative terms, respectively. `b` and `c` values are real, finite, and positive. When you create a 2-DOF PID controller using the `pidstd2` command, the initial values of these properties are set by the `b`, and `c` input arguments, respectively. `Kp` Proportional gain. The value of `Kp` is real and finite. When you create a 2-DOF PID controller using the `pidstd2` command, the initial value of this property is set by the `Kp` input argument. `Ti` Integrator time. `Ti` is real and positive. When you create a 2-DOF PID controller using the `pidstd2` command, the initial value of this property is set by the `Ti` input argument. When `Ti` = `Inf`, the controller has no integral action. `Td` Derivative time. `Td` is real, finite, and nonnegative. When you create a 2-DOF PID controller using the `pidstd2` command, the initial value of this property is set by the `Td` input argument. When `Td` = 0, the controller has no derivative action. `N` Derivative filter divisor. `N` must be real and positive. When you create a 2-DOF PID controller using the `pidstd2` command, the initial value of this property is set by the `N` input argument. `IFormula` Discrete integrator formula IF(z) for the integrator of the discrete-time `pidstd2` controller `C2`. The relationship between the inputs and output of `C2` is given by: `$u={K}_{p}\\left[\\left(br-y\\right)+\\frac{1}{{T}_{i}}IF\\left(z\\right)\\left(r-y\\right)+\\frac{{T}_{d}}{\\frac{{T}_{d}}{N}+DF\\left(z\\right)}\\left(cr-y\\right)\\right].$` `IFormula` can take the following values: `'ForwardEuler'` — IF(z) = $\\frac{{T}_{s}}{z-1}.$This formula is best for small sample time, where the Nyquist limit is large compared to the bandwidth of the controller. For larger sample time, the `ForwardEuler` formula can result in instability, even when discretizing a system that is stable in continuous time.`'BackwardEuler'` — IF(z) = $\\frac{{T}_{s}z}{z-1}.$An advantage of the `BackwardEuler` formula is that discretizing a stable continuous-time system using this formula always yields a stable discrete-time result.`'Trapezoidal'` — IF(z) = $\\frac{{T}_{s}}{2}\\frac{z+1}{z-1}.$An advantage of the `Trapezoidal` formula is that discretizing a stable continuous-time system using this formula always yields a stable discrete-time result. Of all available integration formulas, the `Trapezoidal` formula yields the closest match between frequency-domain properties of the discretized system and the corresponding continuous-time system. When `C2` is a continuous-time controller, `IFormula` is `''`. Default: `'ForwardEuler'` `DFormula` Discrete integrator formula DF(z) for the derivative filter of the discrete-time `pidstd2` controller `C2`. The relationship between the inputs and output of `C2` is given by: `$u={K}_{p}\\left[\\left(br-y\\right)+\\frac{1}{{T}_{i}}IF\\left(z\\right)\\left(r-y\\right)+\\frac{{T}_{d}}{\\frac{{T}_{d}}{N}+DF\\left(z\\right)}\\left(cr-y\\right)\\right].$` `DFormula` can take the following values: `'ForwardEuler'` — DF(z) = $\\frac{{T}_{s}}{z-1}.$This formula is best for small sample time, where the Nyquist limit is large compared to the bandwidth of the controller. For larger sample time, the `ForwardEuler` formula can result in instability, even when discretizing a system that is stable in continuous time.`'BackwardEuler'` — DF(z) = $\\frac{{T}_{s}z}{z-1}.$An advantage of the `BackwardEuler` formula is that discretizing a stable continuous-time system using this formula always yields a stable discrete-time result.`'Trapezoidal'` — DF(z) = $\\frac{{T}_{s}}{2}\\frac{z+1}{z-1}.$An advantage of the `Trapezoidal` formula is that discretizing a stable continuous-time system using this formula always yields a stable discrete-time result. Of all available integration formulas, the `Trapezoidal` formula yields the closest match between frequency-domain properties of the discretized system and the corresponding continuous-time system.The `Trapezoidal` value for `DFormula` is not available for a `pidstd2` controller with no derivative filter (`N = Inf`). When `C2` is a continuous-time controller, `DFormula` is `''`. Default: `'ForwardEuler'` `InputDelay` Time delay on the system input. `InputDelay` is always 0 for a `pidstd2` controller object. `OutputDelay` Time delay on the system Output. `OutputDelay` is always 0 for a `pidstd2` controller object. `Ts` Sample time. For continuous-time models, `Ts = 0`. For discrete-time models, `Ts` is a positive scalar representing the sampling period. This value is expressed in the unit specified by the `TimeUnit` property of the model. PID controller models do not support unspecified sample time (```Ts = -1```). Changing this property does not discretize or resample the model. Use `c2d` and `d2c` to convert between continuous- and discrete-time representations. Use `d2d` to change the sample time of a discrete-time system. Default: `0` (continuous time) `TimeUnit` Units for the time variable, the sample time `Ts`, and any time delays in the model, specified as one of the following values:`'nanoseconds'``'microseconds'``'milliseconds'``'seconds'` `'minutes'``'hours'``'days'``'weeks'``'months'``'years'` Changing this property has no effect on other properties, and therefore changes the overall system behavior. Use `chgTimeUnit` to convert between time units without modifying system behavior. Default: `'seconds'` `InputName` Input channel name, specified as a character vector or a 2-by-1 cell array of character vectors. Use this property to name the input channels of the controller model. For example, assign the names `setpoint` and `measurement` to the inputs of a 2-DOF PID controller model `C` as follows. `C.InputName = {'setpoint';'measurement'};` Alternatively, use automatic vector expansion to assign both input names. For example: `C.InputName = 'C-input';` The input names automatically expand to `{'C-input(1)';'C-input(2)'}`. You can use the shorthand notation `u` to refer to the `InputName` property. For example, `C.u` is equivalent to `C.InputName`. Input channel names have several uses, including: Identifying channels on model display and plotsSpecifying connection points when interconnecting models Default: `{'';''}` `InputUnit` Input channel units, specified as a 2-by-1 cell array of character vectors. Use this property to track input signal units. For example, assign the units `Volts` to the reference input and the concentration units `mol/m^3` to the measurement input of a 2-DOF PID controller model `C` as follows. `C.InputUnit = {'Volts';'mol/m^3'};` `InputUnit` has no effect on system behavior. Default: `{'';''}` `InputGroup` Input channel groups. This property is not needed for PID controller models. Default: `struct` with no fields `OutputName` Output channel name, specified as a character vector. Use this property to name the output channel of the controller model. For example, assign the name `control` to the output of a controller model `C` as follows. `C.OutputName = 'control';` You can use the shorthand notation `y` to refer to the `OutputName` property. For example, `C.y` is equivalent to `C.OutputName`. Input channel names have several uses, including: Identifying channels on model display and plotsSpecifying connection points when interconnecting models Default: Empty character vector, `''` `OutputUnit` Output channel units, specified as a character vector. Use this property to track output signal units. For example, assign the unit `Volts` to the output of a controller model `C` as follows. `C.OutputUnit = 'Volts';` `OutputUnit` has no effect on system behavior. Default: Empty character vector, `''` `OutputGroup` Output channel groups. This property is not needed for PID controller models. Default: `struct` with no fields `Name` System name, specified as a character vector. For example, `'system_1'`. Default: `''` `Notes` Any text that you want to associate with the system, stored as a string or a cell array of character vectors. The property stores whichever data type you provide. For instance, if `sys1` and `sys2` are dynamic system models, you can set their `Notes` properties as follows: ```sys1.Notes = \"sys1 has a string.\"; sys2.Notes = 'sys2 has a character vector.'; sys1.Notes sys2.Notes``` ```ans = \"sys1 has a string.\" ans = 'sys2 has a character vector.' ``` Default: `[0×1 string]` `UserData` Any type of data you want to associate with system, specified as any MATLAB® data type. Default: `[]` `SamplingGrid` Sampling grid for model arrays, specified as a data structure. For model arrays that are derived by sampling one or more independent variables, this property tracks the variable values associated with each model in the array. This information appears when you display or plot the model array. Use this information to trace results back to the independent variables. Set the field names of the data structure to the names of the sampling variables. Set the field values to the sampled variable values associated with each model in the array. All sampling variables should be numeric and scalar valued, and all arrays of sampled values should match the dimensions of the model array. For example, suppose you create a 11-by-1 array of linear models, `sysarr`, by taking snapshots of a linear time-varying system at times `t = 0:10`. The following code stores the time samples with the linear models. ` sysarr.SamplingGrid = struct('time',0:10)` Similarly, suppose you create a 6-by-9 model array, `M`, by independently sampling two variables, `zeta` and `w`. The following code attaches the `(zeta,w)` values to `M`. ```[zeta,w] = ndgrid(<6 values of zeta>,<9 values of w>) M.SamplingGrid = struct('zeta',zeta,'w',w)``` When you display `M`, each entry in the array includes the corresponding `zeta` and `w` values. `M` ```M(:,:,1,1) [zeta=0.3, w=5] = 25 -------------- s^2 + 3 s + 25 M(:,:,2,1) [zeta=0.35, w=5] = 25 ---------------- s^2 + 3.5 s + 25 ...``` For model arrays generated by linearizing a Simulink® model at multiple parameter values or operating points, the software populates `SamplingGrid` automatically with the variable values that correspond to each entry in the array. For example, the Simulink Control Design™ commands `linearize` (Simulink Control Design) and `slLinearizer` (Simulink Control Design) populate `SamplingGrid` in this way. Default: `[]`\n\n## Examples\n\ncollapse all\n\nCreate a continuous-time 2-DOF PDF controller in standard form. To do so, set the integral time constant to `Inf`. Set the other gains and the filter divisor to the desired values.\n\n```Kp = 1; Ti = Inf; % No integrator Td = 3; N = 6; b = 0.5; % setpoint weight on proportional term c = 0.5; % setpoint weight on derivative term C2 = pidstd2(Kp,Ti,Td,N,b,c)```\n```C2 = s u = Kp * [(b*r-y) + Td * ------------ * (c*r-y)] (Td/N)*s+1 with Kp = 1, Td = 3, N = 6, b = 0.5, c = 0.5 Continuous-time 2-DOF PDF controller in standard form ```\n\nThe display shows the controller type, formula, and parameter values, and verifies that the controller has no integrator term.\n\nCreate a discrete-time 2-DOF PI controller in standard form, using the trapezoidal discretization formula. Specify the formula using `Name,Value` syntax.\n\n```Kp = 1; Ti = 2.4; Td = 0; N = Inf; b = 0.5; c = 0; Ts = 0.1; C2 = pidstd2(Kp,Ti,Td,N,b,c,Ts,'IFormula','Trapezoidal')```\n```C2 = 1 Ts*(z+1) u = Kp * [(b*r-y) + ---- * -------- * (r-y)] Ti 2*(z-1) with Kp = 1, Ti = 2.4, b = 0.5, Ts = 0.1 Sample time: 0.1 seconds Discrete-time 2-DOF PI controller in standard form ```\n\nSetting `Td` = 0 specifies a PI controller with no derivative term. As the display shows, the values of `N` and `c` are not used in this controller. The display also shows that the trapezoidal formula is used for the integrator.\n\nCreate a 2-DOF PID controller in standard form, and set the dynamic system properties `InputName` and `OutputName`. Naming the inputs and the output is useful, for example, when you interconnect the PID controller with other dynamic system models using the `connect` command.\n\n`C2 = pidstd2(1,2,3,10,1,1,'InputName',{'r','y'},'OutputName','u')`\n```C2 = 1 1 s u = Kp * [(b*r-y) + ---- * --- * (r-y) + Td * ------------ * (c*r-y)] Ti s (Td/N)*s+1 with Kp = 1, Ti = 2, Td = 3, N = 10, b = 1, c = 1 Continuous-time 2-DOF PIDF controller in standard form ```\n\nA 2-DOF PID controller has two inputs and one output. Therefore, the `'InputName'` property is an array containing two names, one for each input. The model display does not show the input and output names for the PID controller, but you can examine the property values to see them. For instance, verify the input name of the controller.\n\n`C2.InputName`\n```ans = 2x1 cell {'r'} {'y'} ```\n\nCreate a 2-by-3 grid of 2-DOF PI controllers in standard form. The proportional gain ranges from 1–2 across the array rows, and the integrator time constant ranges from 5–9 across columns.\n\nTo build the array of PID controllers, start with arrays representing the gains.\n\n```Kp = [1 1 1;2 2 2]; Ti = [5:2:9;5:2:9];```\n\nWhen you pass these arrays to the `pidstd2` command, the command returns the array of controllers.\n\n```pi_array = pidstd2(Kp,Ti,0,Inf,0.5,0,'Ts',0.1,'IFormula','BackwardEuler'); size(pi_array)```\n```2x3 array of 2-DOF PID controller. Each PID has 1 output and 2 inputs. ```\n\nIf you provide scalar values for some coefficients, `pidstd2` automatically expands them and assigns the same value to all entries in the array. For instance, in this example, `Td` = 0, so that all entries in the array are PI controllers. Also, all entries in the array have `b` = 0.5.\n\nAccess entries in the array using array indexing. For dynamic system arrays, the first two dimensions are the I/O dimensions of the model, and the remaining dimensions are the array dimensions. Therefore, the following command extracts the (2,3) entry in the array.\n\n`pi23 = pi_array(:,:,2,3)`\n```pi23 = 1 Ts*z u = Kp * [(b*r-y) + ---- * ------ * (r-y)] Ti z-1 with Kp = 2, Ti = 9, b = 0.5, Ts = 0.1 Sample time: 0.1 seconds Discrete-time 2-DOF PI controller in standard form ```\n\nYou can also build an array of PID controllers using the `stack` command.\n\n```C2 = pidstd2(1,5,0.1,Inf,0.5,0.5); % PID controller C2f = pidstd2(1,5,0.1,0.5,0.5,0.5); % PID controller with filter pid_array = stack(2,C2,C2f); % stack along 2nd array dimension```\n\nThese commands return a 1-by-2 array of controllers.\n\n`size(pid_array)`\n```1x2 array of 2-DOF PID controller. Each PID has 1 output and 2 inputs. ```\n\nAll PID controllers in an array must have the same sample time, discrete integrator formulas, and dynamic system properties such as `InputName` and `OutputName`.\n\nConvert a parallel-form `pid2` controller to standard form.\n\nParallel PID form expresses the controller actions in terms of proportional, integral, and derivative gains `Kp`, `Ki`, and `Kd`, and filter time constant `Tf`. You can convert a parallel-form `pid2` controller to standard form using the `pidstd2` command, provided that both of the following are true:\n\n• The `pid2` controller can be expressed in valid standard form.\n\n• The gains `Kp`, `Ki`, and `Kd` of the `pid2` controller all have the same sign.\n\nFor example, consider the following parallel-form controller.\n\n```Kp = 2; Ki = 3; Kd = 4; Tf = 2; b = 0.1; c = 0.5; C2_par = pid2(Kp,Ki,Kd,Tf,b,c)```\n```C2_par = 1 s u = Kp (b*r-y) + Ki --- (r-y) + Kd -------- (c*r-y) s Tf*s+1 with Kp = 2, Ki = 3, Kd = 4, Tf = 2, b = 0.1, c = 0.5 Continuous-time 2-DOF PIDF controller in parallel form. ```\n\nConvert this controller to parallel form using `pidstd2`.\n\n`C2_std = pidstd2(C2_par)`\n```C2_std = 1 1 s u = Kp * [(b*r-y) + ---- * --- * (r-y) + Td * ------------ * (c*r-y)] Ti s (Td/N)*s+1 with Kp = 2, Ti = 0.667, Td = 2, N = 1, b = 0.1, c = 0.5 Continuous-time 2-DOF PIDF controller in standard form ```\n\nThe display confirms the new standard form. A response plot confirms that the two forms are equivalent.\n\n```bodeplot(C2_par,'b-',C2_std,'r--') legend('Parallel','Standard','Location','Southeast')```", null, "Convert a two-input, one-output continuous-time dynamic system that represents a 2-DOF PID controller to a standard-form `pidstd2` controller.\n\nThe following state-space matrices represent a 2-DOF PID controller.\n\n```A = [0,0;0,-8.181]; B = [1,-1;-0.1109,8.181]; C = [0.2301,10.66]; D = [0.8905,-11.79]; sys = ss(A,B,C,D);```\n\nRewrite `sys` in terms of the standard-form PID parameters `Kp`, `Ti`, `Td`, and `N`, and the setpoint weights `b` and `c`.\n\n`C2 = pidstd2(sys)`\n```C2 = 1 1 s u = Kp * [(b*r-y) + ---- * --- * (r-y) + Td * ------------ * (c*r-y)] Ti s (Td/N)*s+1 with Kp = 1.13, Ti = 4.91, Td = 1.15, N = 9.43, b = 0.66, c = 0.0136 Continuous-time 2-DOF PIDF controller in standard form ```\n\nConvert a discrete-time dynamic system that represents a 2-DOF PID controller with derivative filter to standard `pidstd2` form.\n\nThe following state-space matrices represent a discrete-time 2-DOF PID controller with a sample time of 0.05 s.\n\n```A = [1,0;0,0.6643]; B = [0.05,-0.05; -0.004553,0.3357]; C = [0.2301,10.66]; D = [0.8905,-11.79]; Ts = 0.05; sys = ss(A,B,C,D,Ts);```\n\nWhen you convert `sys` to 2-DOF PID form, the result depends on which discrete integrator formulas you specify for the conversion. For instance, use the default, `ForwardEuler`, for both the integrator and the derivative.\n\n`C2fe = pidstd2(sys)`\n```C2fe = 1 Ts 1 u = Kp * [(b*r-y) + ---- * ------ * (r-y) + Td * --------------- * (c*r-y)] Ti z-1 (Td/N)+Ts/(z-1) with Kp = 1.13, Ti = 4.91, Td = 1.41, N = 9.43, b = 0.66, c = 0.0136, Ts = 0.05 Sample time: 0.05 seconds Discrete-time 2-DOF PIDF controller in standard form ```\n\nNow convert using the `Trapezoidal` formula.\n\n`C2trap = pidstd2(sys,'IFormula','Trapezoidal','DFormula','Trapezoidal')`\n```C2trap = 1 Ts*(z+1) 1 u = Kp * [(b*r-y) + ---- * -------- * (r-y) + Td * ----------------------- * (c*r-y)] Ti 2*(z-1) (Td/N)+Ts/2*(z+1)/(z-1) with Kp = 1.12, Ti = 4.89, Td = 1.41, N = 11.4, b = 0.658, c = 0.0136, Ts = 0.05 Sample time: 0.05 seconds Discrete-time 2-DOF PIDF controller in standard form ```\n\nThe displays show the difference in resulting coefficient values and functional form.\n\nFor some dynamic systems, attempting to use the `Trapezoidal` or `BackwardEuler` integrator formulas yields invalid results, such as negative `Ti`, `Td`, or `N` values. In such cases, `pidstd2` returns an error.\n\nDiscretize a continuous-time standard-form 2-DOF PID controller and specify the integral and derivative filter formulas.\n\nCreate a continuous-time `pidstd2` controller and discretize it using the zero-order-hold method of the `c2d` command.\n\n```C2con = pidstd2(10,5,3,0.5,1,1); % continuous-time 2-DOF PIDF controller C2dis1 = c2d(C2con,0.1,'zoh')```\n```C2dis1 = 1 Ts 1 u = Kp * [(b*r-y) + ---- * ------ * (r-y) + Td * --------------- * (c*r-y)] Ti z-1 (Td/N)+Ts/(z-1) with Kp = 10, Ti = 5, Td = 3.03, N = 0.5, b = 1, c = 1, Ts = 0.1 Sample time: 0.1 seconds Discrete-time 2-DOF PIDF controller in standard form ```\n\nThe display shows that `c2d` computes new PID coefficients for the discrete-time controller.\n\nThe discrete integrator formulas of the discretized controller depend on the `c2d` discretization method, as described in Tips. For the `zoh` method, both `IFormula` and `DFormula` are `ForwardEuler`.\n\n`C2dis1.IFormula`\n```ans = 'ForwardEuler' ```\n`C2dis1.DFormula`\n```ans = 'ForwardEuler' ```\n\nIf you want to use different formulas from the ones returned by `c2d`, then you can directly set the `Ts`, `IFormula`, and `DFormula` properties of the controller to the desired values.\n\n```C2dis2 = C2con; C2dis2.Ts = 0.1; C2dis2.IFormula = 'BackwardEuler'; C2dis2.DFormula = 'BackwardEuler';```\n\nHowever, these commands do not compute new coefficients for the discretized controller. To see this, examine `C2dis2` and compare the coefficients to `C2con` and `C2dis1`.\n\n`C2dis2`\n```C2dis2 = 1 Ts*z 1 u = Kp * [(b*r-y) + ---- * ------ * (r-y) + Td * ----------------- * (c*r-y)] Ti z-1 (Td/N)+Ts*z/(z-1) with Kp = 10, Ti = 5, Td = 3, N = 0.5, b = 1, c = 1, Ts = 0.1 Sample time: 0.1 seconds Discrete-time 2-DOF PIDF controller in standard form ```\n\n## Tips\n\n• To design a PID controller for a particular plant, use `pidtune` or `pidTuner`. To create a tunable 2-DOF PID controller as a control design block, use `tunablePID2`.\n\n• To break a 2-DOF controller into two SISO control components, such as a feedback controller and a feedforward controller, use `getComponents`.\n\n• Create arrays of `pidstd2` controllers by:\n\nIn an array of `pidstd2` controllers, each controller must have the same sample time `Ts` and discrete integrator formulas `IFormula` and `DFormula`.\n\n• To create or convert to a parallel-form controller, use `pid2`. Parallel form expresses the controller actions in terms of proportional, integral, and derivative gains Kp, Ki and Kd, and a filter time constant Tf. For example, the relationship between the inputs and output of a continuous-time parallel-form 2-DOF PID controller is given by:\n\n`$u={K}_{p}\\left(br-y\\right)+\\frac{{K}_{i}}{s}\\left(r-y\\right)+\\frac{{K}_{d}s}{{T}_{f}s+1}\\left(cr-y\\right).$`\n• There are two ways to discretize a continuous-time `pidstd2` controller:\n\n• Use the `c2d` command. `c2d` computes new parameter values for the discretized controller. The discrete integrator formulas of the discretized controller depend upon the `c2d` discretization method you use, as shown in the following table.\n\n`c2d` Discretization Method`IFormula``DFormula`\n`'zoh'``ForwardEuler``ForwardEuler`\n`'foh'``Trapezoidal``Trapezoidal`\n`'tustin'``Trapezoidal``Trapezoidal`\n`'impulse'``ForwardEuler``ForwardEuler`\n`'matched'``ForwardEuler``ForwardEuler`\n\nFor more information about `c2d` discretization methods, See the `c2d` reference page. For more information about `IFormula` and `DFormula`, see Properties .\n\n• If you require different discrete integrator formulas, you can discretize the controller by directly setting `Ts`, `IFormula`, and `DFormula` to the desired values. (See Discretize a Standard-Form 2-DOF PID Controller.) However, this method does not compute new gain and filter-constant values for the discretized controller. Therefore, this method might yield a poorer match between the continuous- and discrete-time `pidstd2` controllers than using `c2d`.\n\n## Version History\n\nIntroduced in R2015b" ]

[ null, "https://nl.mathworks.com/help/control/ref/pid2dofarch.png", null, "https://nl.mathworks.com/help/examples/control/win64/Convert2DOFPIDControllerFromParallelToStandardFormExample_01.png", null ]

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Just plug in the equation and the correct answer shows.\nPosted on Categories discrete math\n\n## Step by Step Linear Algebra app for the Ti-Nspire CAS CX", null, "Overview and Examples : https://youtu.be/uqIRhvqqVDE\n\nPerform 30+ Matrix Computations such as A+B, A-B, k*A, A*B, B*A, A-1, det(A), Eigenvalues, LU and QR – Factorization, Norm, Trace.\n\n• Step by Step – Simplex Algorithm.\n• Step by Step – Gaussian Elimination.\n• Step by Step – Find Inverse\n• Step by Step – Find Determinant\n• Step by Step – Row Echelon and Reversal (REF and RREF)\n• Step by Step – Gauss and Gauss Jordan Elimination\n• Step by Step – Cramer Rule\n• Step by Step – EigenValues and EigenVectors.\n• Step by Step – Square Root Matrix\n• Solve any n by n system of equations.\n• Rotation Matrices, Magic Squares and much more.\n• Step by Step – Solve AX=B\n• Step by Step – OrthoNormal Basis\n• Step by Step – Range, Kernel\n• Nullity, Null-, Row- and ColumnSpace Basis.\n• Cross and Dot Product, UnitVector, Angle between Vectors\n• Projection A onto B, Distance A to B, etc …\nPosted on Categories linear algebra\n\n## Step by Step Trigonometry app for the Ti-Nspire CX available now", null, "Watch this Youtube Video at https://youtu.be/nvvWKzVBgfA\n\nSTEP BY STEP – Solve any 90oand non 90o Triangle.Just enter 2 sides and an angle, 3 sides or 1 side and 2 angles to view each step until triangle is solved.\n\n• This app is intelligent enough to automatically apply the Law of Sine or the Law of Cosine and other basic Triangle Rules to solve any triangle STEP by STEP.\n• It even notifies if triangle cannot be solved or solutions are ambiguous.\n• Read the Trig-Theorems and Identities.\n• Evaluate Trig Functions and set up Trig-Models.\n• Master the Unit-Circle and its Coordinates.\n• Compute Sectors and Arcs.\n• Convert Degree to Radian and vice versa.\n• STEP BY STEP – Given Sin Cos or Tan find the remaining ratios in a 90 degree triangle.\n• Right Triangle Checker: Check For Right Angle given 3 points\n• Trig Identity Checker\n• Convert Degrees(decimals) to Degrees, Minutes, Seconds\n• Convert Cartesian Coordinates to Polar Coordinates and vice versa.\n\nWatch how to use the app when doing Trig homework at http://<iframe width=”460″ height=”335″ src=”https://www.youtube.com/embed/RSHEQztJdw4″ frameborder=”0″ allowfullscreen></iframe>\n\nPosted on Categories trigonometry\n\n## Step by Step PreCalculus app for the Ti-Nspire CAS CX available now", null, "Watch this Youtube Video for an overview and examples at https://youtu.be/cRIs3oUicrw\n\nComplete and Comprehensive.\n\nStep by Step Solutions to : Functions (Polynomial, Exponential, Logarithmic and Trigonometric Functions), Trigonometry, Statistics, Discrete Mathematics, Algebra, Matrices, Complex Numbers, Sequences, Introductory Calculus.\n\nWatch this Video on using the app doing PreCalculus homework at https://youtu.be/B9bYtG52XE4\n\n## Step by Step Algebra app for the Ti-Nspire – Watch this Video at https://youtu.be/Q0uXzdzzHog\n\nStep by Step Algebra App for the Ti-NSpire at www.tinspireapps.com. It covers the ENTIRE Algebra curriculum: Algebra, Functions and their Analysis, Trig, Geometry, Complex Numbers, Matrices, Exponential/Logarithmic Functions, Probabilities, Combinatorics, Sequences, Induction, Sigma Notation, etc\n\n• Step by Step – Complete the Square\n• Step by Step – Partial Fractions\n• Step by Step – Complex Numbers\n• Step by Step – Powers\n• Step by Step – Roots\n• Step by Step – Synthetic Division\n• Step by Step – Radicals\n• Logarithm and Exponential Solver\n• Rewrite Logarithms into their Exponential Form and back: log_b(y)=x <–> y=b^x\n• Expand and Condense Logarithms Step by Step\n• Rule of 72, Change of Logarithm base\n• Effective Interest rates\n• Euler Number as Limit Definition.\n• Money Growth Solver\n\n## Step by Step Differential Equations app for the Ti-Spire – Watch this Video at https://youtu.be/7lH9GrSv2jAO8\n\nGreat News: Step by step Differential Equations App for the TiNspire is now available for download at www.tinspireapps.com . It includes:\n\n• Step by Step Linear Diff Eqn\n• Step by Step Variation of Parameter\n• Step by Step Linear Undetermined Coefficients\n• Step by Step Separation of Variables\n• Step by Step Exact and Non-Exact Diff Eqns\n• Step by Step Laplace Transforms\n• Step by Step Wronskian\n• Step by Step Cauchy Euler Diff Eqns\n• Step by Step Numerical Solutions : Euler, Runge Kutta\n• Step by Step Homogeneous Diff Eqns. and Characteristic Polynomial\n• Step by Step Eigenvalues and Eigenvectors\n• Step by Step Logistic Growth Diff. Equation\n• and much more.\n\nPosted on Categories differential equation\n\n## Step by Step Chemistry app now available for the TI-Nspire CX CAS\n\nTI-Nspire users:\n\nStep by Step Chemistry problems involving\n\nPeriod Table of Elements,\n\nEquation Balancing,\n\nStoichiometry,\n\nTheoretical and %-Yield\n\nLimiting Reagent\n\nHess Law\n\nMolecule Mass Analysis\n\nGas Laws,\n\nMoles, Mass, Density, Volume, Weight etc\n\nFree trials." ]

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[ "", null, "# Ellipse Visualization¶\n\nToyplot supports drawing oriented ellipses using toyplot.coordinates.Cartesian.ellipse(). Ellipses are defined using their center, x and y radius, and angle with respect to the X axis. For example, to create an unrotated ellipse centered at the origin:\n\n:\n\nimport toyplot\n\ncanvas = toyplot.Canvas(width=400)\naxes = canvas.cartesian(aspect=\"fit-range\")\naxes.ellipse(0, 0, 5, 2);\n\n\nWhen rotating ellipses, angles are specified in degrees with positive angles leading to clockwise rotation:\n\n:\n\ncanvas = toyplot.Canvas(width=400)\naxes = canvas.cartesian(aspect=\"fit-range\")\naxes.ellipse(0, 0, 5, 2, 45);\n\n\nOf course, you can use color, opacity, and style to alter the appearance of an ellipse:\n\n:\n\ncanvas = toyplot.Canvas(width=600, height=300)\naxes = canvas.cartesian(grid=(1, 2, 0), aspect=\"fit-range\")\naxes.ellipse(0, 0, 5, 2, 45, color=\"crimson\", opacity=0.5)\naxes = canvas.cartesian(grid=(1, 2, 1), aspect=\"fit-range\")\naxes.ellipse(0, 0, 5, 2, 45, style={\"stroke\": \"black\", \"fill\":\"none\"});\n\n\nOne thing to keep in mind when working with ellipses is that, if you don’t specify an explicit domain for your axes, Toyplot’s default axis scaling will tend to turn an ellipse into a circle:\n\n:\n\ncanvas = toyplot.Canvas(width=300)\naxes = canvas.cartesian() # Allow Toyplot to choose the domain\naxes.ellipse(0, 0, 5, 2);\n\n\nThis is because Toyplot treats your ellipses as data - that is, ellipses aren’t just symbols drawn atop the canvas, they are embedded in the space defined by the axes. Thus, an ellipse will be distorted when viewed using a nonlinear projection such as log axes. This is by design:\n\n:\n\ncanvas = toyplot.Canvas(width=600, height=300)\naxes = canvas.cartesian(grid=(1, 2, 0), label=\"Linear Y projection\")\naxes.ellipse(20, 15, 20, 5, 30)\naxes = canvas.cartesian(grid=(1, 2, 1), yscale=\"log\", label=\"Nonlinear Y projection\")\naxes.ellipse(20, 15, 20, 5, 30);\n\n\nThe distortion can become even more extreme if the ellipse straddles the origin:\n\n:\n\ncanvas = toyplot.Canvas(width=600, height=300)\naxes = canvas.cartesian(grid=(1, 2, 0), label=\"Linear Y projection\")\naxes.ellipse(0, 0, 20, 5, 30)\naxes = canvas.cartesian(grid=(1, 2, 1), yscale=\"log\", label=\"Nonlinear Y projection\")\naxes.ellipse(0, 0, 20, 5, 30);\n\n\nWhile this behavior may seem nonintuitive at first, it makes sense when you’re using an ellipse to visualize confidence or other bounds for sampled data. For example, suppose you’re drawing samples from a bivariate normal distribution:\n\n:\n\nimport numpy\nnumpy.random.seed(1234)\n\nmean = numpy.array([3, 5])\ncovariance = numpy.array([[3, 1], [1, 1]])\n\nsamples = numpy.random.multivariate_normal(mean, covariance, size=1000)\n\ncanvas = toyplot.Canvas()\naxes = canvas.cartesian(aspect=\"fit-range\")\naxes.scatterplot(samples[:,0], samples[:,1]);\n\n\nIf you wanted to draw ellipses at 1, 2, and 3-$$\\sigma$$ intervals, you might do the following:\n\n:\n\neigenvalues, eigenvectors = numpy.linalg.eig(covariance)\nangle = numpy.degrees(numpy.arctan2(eigenvectors[1, 0], eigenvectors[0, 0]))\n\nxsigma = numpy.sqrt(eigenvalues)\nysigma = numpy.sqrt(eigenvalues)\n\ncanvas = toyplot.Canvas()\naxes = canvas.cartesian(aspect=\"fit-range\")\naxes.scatterplot(samples[:,0], samples[:,1])\naxes.ellipse(mean, mean, xsigma, ysigma, angle, style={\"stroke\":\"black\", \"fill\":\"none\"})\naxes.ellipse(mean, mean, xsigma * 2, ysigma * 2, angle, style={\"stroke\":\"black\", \"fill\":\"none\"})\naxes.ellipse(mean, mean, xsigma * 3, ysigma * 3, angle, style={\"stroke\":\"black\", \"fill\":\"none\"});\n\n\nHowever, if you use a nonlinear projection on the Y axis, the ellipse needs to deform along with the rest of the data:\n\n:\n\ncanvas = toyplot.Canvas(width=600, height=400)\naxes = canvas.cartesian(aspect=\"fit-range\", yscale=\"log\")\naxes.scatterplot(samples[:,0], samples[:,1])\naxes.ellipse(mean, mean, xsigma, ysigma, angle, style={\"stroke\":\"black\", \"fill\":\"none\"})\naxes.ellipse(mean, mean, xsigma * 2, ysigma * 2, angle, style={\"stroke\":\"black\", \"fill\":\"none\"})\naxes.ellipse(mean, mean, xsigma * 3, ysigma * 3, angle, style={\"stroke\":\"black\", \"fill\":\"none\"});\n\n\nFinally, as with other Toyplot visualizations, you are not limited to creating individual ellipses one-at-a-time - you can create a series of ellipses in a single call:\n\n:\n\nnumpy.random.seed(14)\n\nx = numpy.random.uniform(-6, 6, size=10)\ny = numpy.random.uniform(-4, 4, size=10)\nrx = numpy.random.uniform(0.1, 1, size=10)\nry = numpy.random.uniform(0.1, 1, size=10)\nangle = numpy.random.uniform(0, 180, size=10)\n\ncanvas = toyplot.Canvas(width=600, height=400)\naxes = canvas.cartesian(aspect=\"fit-range\")\naxes.ellipse(x, y, rx, ry, angle, color=toyplot.color.brewer.map(\"Set1\"), style={\"stroke\":\"white\"});" ]

[ null, "https://toyplot.readthedocs.io/en/stable/_images/toyplot.png", null ]

[ "You Are Here:\n\nMath is more than memorizing formulas and doing calculations. Math involves:\n\n• Highly practical and hands-on problems and skills\n• Rich problem-solving activities in collaboration with your peers\n• Some problems that will stretch your understanding to the abstract and theoretical\n• Using technology to develop, demonstrate and communicate your mathematical understandings\n\n### Mathematics 9\n\nThis course covers the major strands of math from the Alberta curriculum. Students are introduced to the mathematics topics of numbers, algebra, trigonometry, geometry, transformations and probability. There is a Provincial Achievement Test for all students at the end of June of their grade nine year.\n\n### Math 10C (5 credits)\n\nThis course has been designed to facilitate a smoother transition between Grade 9 and 10 Mathematics. Students will have one course of high school math before deciding whether to register in Math 20-1 or Math 20-2. Guidance will be provided to students about which sequence to select depending on their grades and their post-secondary plans. Topics covered in this course are number and powers, algebra and polynomials, measurement and trigonometry.\n\n### Math 20-1 “Precalculus” (5 credits)\n\nPrerequisite: Math 10C with a recommended mark of 70%. This course sequence is designed to provide students with the mathematical understandings and critical-thinking skills identified for entry into post-secondary programs that require the study of calculus. Topics include algebra and number; measurement; relations and functions, and trigonometry.\n\n### Math 20-2 “Foundations of Mathematics” (5 credits)\n\nPrerequisite: Math 10C. This course sequence is designed to provide students with the mathematical understandings and critical-thinking skills identified for post-secondary studies in programs that do not require the study of calculus. Topics include geometry, measurement, number and logic, logical reasoning, relations and functions, statistics, and probability.\n\n### Math 30-1 “Pre-Calculus” (5 credits)\n\nPrerequisite: MATH 20-1 with a recommended mark above 70%. This course sequence is designed to provide students with the mathematical understandings and critical-thinking skills identified for entry into postsecondary programs that require the study of calculus. Topics include relations and functions, permutations and combinations, binomial theorem and trigonometry.\n\n### Math 30-2 “Foundations of Mathematics” (5 Credits)\n\nPrerequisite: Math 20-1 or Math 20-2. This course sequence is designed to provide students with the mathematical understandings and critical thinking skills identified for post-secondary studies in programs that do not require the study of calculus. Topics include Logical Reasoning, Relations and Functions and Probability.\n\n### Mathematics 31 – (5 credits)\n\nPre-requisite: MATH 30-1 with a recommended mark above 80%. This is a first course in Calculus. It is designed for highly motivated students who have a strong interest in mathematics or want to explore courses requiring calculus at university, technical institute or at the college level. Students interested in engineering, physical sciences, or medical sciences should consider taking Math 31.\n\n# Math\n\nMath is more than memorizing formulas and doing calculations. Math involves:\n\n• Highly practical and hands-on problems and skills\n• Rich problem-solving activities in collaboration with your peers\n• Some problems that will stretch your understanding to the abstract and theoretical\n• Using technology to develop, demonstrate and communicate your mathematical understandings\n\n### Mathematics 9\n\nThis course covers the major strands of math from the Alberta curriculum. Students are introduced to the mathematics topics of numbers, algebra, trigonometry, geometry, transformations and probability. There is a Provincial Achievement Test for all students at the end of June of their grade nine year.\n\n### Math 10C (5 credits)\n\nThis course has been designed to facilitate a smoother transition between Grade 9 and 10 Mathematics. Students will have one course of high school math before deciding whether to register in Math 20-1 or Math 20-2. Guidance will be provided to students about which sequence to select depending on their grades and their post-secondary plans. Topics covered in this course are number and powers, algebra and polynomials, measurement and trigonometry.\n\n### Math 20-1 “Precalculus” (5 credits)\n\nPrerequisite: Math 10C with a recommended mark of 70%. This course sequence is designed to provide students with the mathematical understandings and critical-thinking skills identified for entry into post-secondary programs that require the study of calculus. Topics include algebra and number; measurement; relations and functions, and trigonometry.\n\n### Math 20-2 “Foundations of Mathematics” (5 credits)\n\nPrerequisite: Math 10C. This course sequence is designed to provide students with the mathematical understandings and critical-thinking skills identified for post-secondary studies in programs that do not require the study of calculus. Topics include geometry, measurement, number and logic, logical reasoning, relations and functions, statistics, and probability.\n\n### Math 30-1 “Pre-Calculus” (5 credits)\n\nPrerequisite: MATH 20-1 with a recommended mark above 70%. This course sequence is designed to provide students with the mathematical understandings and critical-thinking skills identified for entry into postsecondary programs that require the study of calculus. Topics include relations and functions, permutations and combinations, binomial theorem and trigonometry.\n\n### Math 30-2 “Foundations of Mathematics” (5 Credits)\n\nPrerequisite: Math 20-1 or Math 20-2. This course sequence is designed to provide students with the mathematical understandings and critical thinking skills identified for post-secondary studies in programs that do not require the study of calculus. Topics include Logical Reasoning, Relations and Functions and Probability.\n\n### Mathematics 31 – (5 credits)\n\nPre-requisite: MATH 30-1 with a recommended mark above 80%. This is a first course in Calculus. It is designed for highly motivated students who have a strong interest in mathematics or want to explore courses requiring calculus at university, technical institute or at the college level. Students interested in engineering, physical sciences, or medical sciences should consider taking Math 31." ]

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[ "Cody\n\n# Problem 2168. Positive Infinity\n\nSolution 999695\n\nSubmitted on 6 Oct 2016 by CY Y\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\n### Test Suite\n\nTest Status Code Input and Output\n1   Pass\na = [2.5 -1.7 5.6 8.4] y_correct = [ 3 -1 6 9]; assert(isequal(positiveround(a),y_correct)) a = [ -105.25 78.89 -0.1 0.9 7.2] y_correct = [ -105 79 0 1 8] assert(isequal(positiveround(a),y_correct)) a = [ 265.25 88.99 -0.1 0.9 7.2] y_correct = [ 266 89 0 1 8] assert(isequal(positiveround(a),y_correct))\n\na = 2.5000 -1.7000 5.6000 8.4000 y = 3 -1 6 9 a = -105.2500 78.8900 -0.1000 0.9000 7.2000 y_correct = -105 79 0 1 8 y = -105 79 0 1 8 a = 265.2500 88.9900 -0.1000 0.9000 7.2000 y_correct = 266 89 0 1 8 y = 266 89 0 1 8\n\n### Community Treasure Hunt\n\nFind the treasures in MATLAB Central and discover how the community can help you!\n\nStart Hunting!" ]

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[ "We’re rewarding the question askers & reputations are being recalculated! Read more.\n\n# Tag Info\n\n26\n\nThere is still a search for problems where the D-Wave shows improvement over classical algorithms. One might recall media splashes where the D-Wave solved some instances $10^8$ times faster than a classical algorithms but forgot to mention that the problem can be solved in polynomial time using minimum weight perfect matching. Denchev showing $10^8$ ...\n\n18\n\nA Quantum Annealer, such as a D-Wave machine is a physical representation of the Ising model and as such has a 'problem' Hamiltonian of the form $$H_P = \\sum_{J=1}^nh_j\\sigma_j^z + \\sum_{i, j}J_{ij}\\sigma_i^z\\sigma_j^z.$$ Essentially, the problem to be solved is mapped to the above Hamiltonian. The system starts with the Hamiltonian $H_I = \\sum_{J=1}^nh'_j\\... 16 Annealing's more of an analog tactic. The gist is that you have some weird function that you want to optimize. So, you bounce around it. At first, the \"temperature\" is very high, such that the selected point can bounce around a lot. Then as the algorithm \"cools\", the temperature goes down, and the bouncing becomes less aggressive. Ultimately, it settles ... 15 First, let me note that quantum annealing, or more precisely the adiabatic quantum computation model is polynomially equivalent to the conventional gate-based quantum computation model. Second, the general traveling salesman problem is NP complete. Third, it is generally believed that the with gate-based quantum computation one cannot solve in polinomial ... 14 The time to solution (tts) is highly dependent on the Hamiltonian of the problem one would like to solve. The D-Wave uses a spin-glass-like Hamiltonian which can be in the NP-Complete complexity class. Due to having to run the annealing process multiple times, tts measures are typically quantified by how long it takes to find the ground state some percent ... 13 In adiabatic QC, you encode your problem in a Hamiltonian such that your result can be extracted from the ground state. Preparing that ground state is hard to do directly, so you instead prepare the ground state of an 'easy' Hamiltonian, and then slowly interpolate between the two. If you go slow enough, the state of your system will stay in the ground state.... 12 As Troyer and Lidar saw no speed increase with the D-Wave 1 compared to classical computers, the D-Wave 2 benchmark figure reported in 2013 of 3600 times as fast as CPLEX (the best algorithm on a conventional machine) suggests the D-Wave 2 is 3600 times as fast as the D-Wave 1. However: the results are in a pretty restricted set of parameters, so this may ... 7 I'll do my best to address your three points. My previous answer to an earlier question about the difference between quantum annealing and adiabatic quantum computation can be found here. I'm in agreement with Lidar that quantum annealing can't be defined without considerations of algorithms and hardware. That being said, the canonical framework for ... 7 As far as I know the closest answer to your question for applications is given in the recent (still unpublished) work presented at the March meeting by Bibek Pokharel, where he compares graph 3-coloring instances on D-Wave Two, D-Wave 2X and D-Wave 2000Q, all other things staying reasonably equal. The short answer is that all the performance increase is ... 6 Yes. This has been done by Morita and Nishimori in their 2008 publication, \"Mathematical Foundations of Quantum Annealing.\" https://arxiv.org/abs/0806.1859 In Section 5 they derive the convergence conditions from path integral Monte Carlo and Green function Monte Carlo methods. To quote; In Sec. 5 we have derived the convergence condition of QA ... 6 Is there proof that the D-wave (one) is a quantum computer and is effective? D-Wave Video - Offers an explanation of: \"How do we know ...\": https://youtu.be/kq9VqR0ZGNc One analogy you might make with the D-Wave One, an adiabatic ('analog') computer, is to the \"south-pointing chariot\" or the \"Antikythera mechanism\". A lengthy explanation is offered in ... 5 Vinci and Lidar have a nice explanation in their introduction of non-stoquastic Hamiltonians in quantum annealing (which is necessary to a quantum annealing device to simulate gate model computation). https://arxiv.org/abs/1701.07494 It is well known that the solution of computational problems can be encoded into the ground state of a time-dependent ... 5 The earliest non-internal reference I can find is in NIPS 2009 from a Google/D-Wave effort1. You'll notice that the two Choi papers, in addition to not using the term \"Chimera\", do not describe a Chimera graph (and note that the name comes from D-Wave, not from graph theory). For a good early reference on Chimera, I recommend Bunyk et al., 20141 , which ... 4 If two matrices (in this case, Hamiltonians) commute, they have the same eigenvectors. So, if you prepare a ground state of the first Hamiltonian, then that will (roughly speaking) remain an eigenstate throughout the whole adiabatic evolution, and so you get out just what you put in. There's no value to it. If you want to be a little more strict, then it ... 4 Until recently, D-Wave's quantum annealing devices always started from a uniform superposition over all$N$qubits: &... 3 One of the advantages, as stated in the paper you linked, is that with QAOA you can increase the precision arbitrarily, whereas QA will only find the solution with probability 1 as$T \\to \\infty$which is impractical. In addition if$T$is too long you're likely to not find the solution as the probability is not monotonic. I believe an example of this can be ... 3 Quantum annealing as defined by Chakrabarti 1981 and later implemented by Kadowaki and Nishimori 1998 uses a varying transverse magnetic field to facilitate tunneling through the energy landscape of an optimization problem. The system is prepared in the ground state of a Hamiltonian and then the transverse field is applied and slowly reduced (adiabatically) ... 3 In the context of Ising optimizers having an initial Hamiltonian that commutes with the problem Hamiltonian means it is essentially products of$\\sigma^Z$operators, which means that its eigenstates are classical bitstrings. Hence the groundstate at the beginning ($t$=0) will be classical as well, not a superposition of all possible bitstrings. Moreover, ... 3 There are multiple factors that affect an embedding's performance, including what Davide mentions. Depending on your background, the following interpretation of Davide's answer might be easier for you to understand: Early in the anneal, the Ising (classical/user-input/final) Hamiltonian has no effect, which means that two spins in a chain are not compelled ... 3 On parameter setting, check our work: https://journals.aps.org/prx/abstract/10.1103/PhysRevX.5.031040 (Basically you want to make sure that the chains representing the logical qubit have a phase transition synchronized with the minimum gap). But in general this is a hard problem, and precision issues connected to the embedding characteristics are probably ... 2 I will assume you are asking about D-Wave's quantum annealer. If there is a part of the learning process that can fit the QUBO (Quadratic Unconstrained Binary Optimization) formulation, then yes. The problem however is what to consider as binary variables of your problem. In CNN, we have in general real-valued parameters that we tweak for training (using ... 2 A couple papers are out there on algorithms which can be constructed using reverse annealing, http://iopscience.iop.org/article/10.1088/1367-2630/aa59c4/meta and https://arxiv.org/abs/1609.05875 (it is worth pointing out previous somewhat related closed system work: https://link.springer.com/article/10.1007/s11128-010-0168-z). As far as experimental results, ... 2 Well first you will have to specify the MST in a QUBO/Ising formulation. In this article showing formulations for different types of problems, section 8.1 is about the MST with a maximal degree constraint. This paper contains results of Spanning Tree calculations. When you have the formulation, you map it on the Chimera Graph if the hardware size is not ... 1 The errors from quantum annealing apart from having crappy qubits will come from the imperfect instantiation of the qubit coupling. The first problem i.e having bad qubits can ultimately be mitigated by a kind of error correction look at Error-corrected quantum annealing with hundreds of qubits (Pudenz et al., 2014). But as it turns out the second problem ... 1 You can use a technique of reduction by substitution. Here we represent using ancilla representing a Boolean constraint$ z\\Leftrightarrow x_1\\wedge x_2 $as a quadratic penalty function : $$P(x_1,x_2;z) = x_1 x_2 - 2(x_1+x_2)z + 3z$$ For a triplet interaction, you use it to reduce to pairwise :$$x_1 x_2 x_3 = \\min_z \\bigl\\{ z x_3 + M P(x_1,x_2;z) \\bigr\\},... 1 You need to introduce ancillary variables and minimize over them; which would enable you to have a QUBO form with only pairing terms. For example, if your binary variables are called$ x,y,z $and you have a$ a*xyz $term with the coefficient$ a$, you can use a technique of reduction by minimum selection where you introduce another variable$w\\$ such that ...\n\n1\n\nThis answer reflects my understanding of what D-wave have to say about this, in the 2013 whitepaper they link to: Programming With D-Wave: Map Coloring Problem To back up the question, we find once again the claim: \"superposition\" states [...] give a quantum computer the ability to quickly solve certain classes of complex problems such as optimization, ...\n\nOnly top voted, non community-wiki answers of a minimum length are eligible" ]

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[ "Está en la página 1de 15\n\n# SPWLA SIXTEENTH ANNUAL LOGGING SYMPOSIUM, JUNE 4-7, 1975\n\n## THE DISTRIBUTION OF SHALE IN SANDSTONES\n\nAND ITS EFFECT UPON POROSITY\n\nBY\n\nE. C. Thomas\nShell Oil Company\nNew Orleans, Louisiana\n\nS. J. Stieber\nButler, Miller & Lents\nHouston, Texas\n\nABSTRACT\n\n## A shale volume parameter derived from the response of\n\nthe gamma ray log in shaly sands is often used to correct the\nresponses of other logs for the effects of the shale. The cor-\nrelation of a garmna ray parameter to shale volume is usually\npresented as one direct relationship. However, because the shale\ncan be distributed through the sand in different ways, such as\nlaminated, dispersed, structural, or any combination of these,\none may expect vasying gamma ray responses dependent upon\ngeometry. We show that each of these configurations can involve\na different response from the gamma ray and this variable response\ncan be used to determine the shale configuration. A gamma ray\nparameter vs. porosity crossplot can then be used to determine\nshale configuration, sand fraction and sand porosity; the derived\nequations can be used for implicit solution when processing\ndigital log data. These configurational data can be combined\nwith electric log parameters to determine the oil saturation of\nthe net sand. These log derived parameters are herein verified\nby direct comparison to rubber sleeve core data.\n\n## The sparcity of porosity logs in many of the older South Louisiana\n\nfields often necessitates that other available log data be correlated to\nporosity. One log which is generally available is the gamma ray collar log\nwhich is used to perforate the well. Thus, empirical gamma ray response -\nDensity log porosity correlations in a particular reservoir are developed\nusing recent penetrations, and this correlation is applied to the older\ngamma ray logs to determine a reservoir-wide porosity distribution. This\nsimple approach is fruitful for reservoirs which are found in Tertiary\nsand-shale sequences and usually will not apply to more complicated miner-\nalogies involving carbonates. An example of this type of correlation is\nshown in Figure 1.\n\nT\n-l-\nSPWLA SIXTEENTH ANNUAL LOGGING SYMPOSIUM, JUNE 4-7, 1975\n\n## It is assumed from the above that shale is the main destroyer\n\nof sand porosity and it is therefore reasonable to expect the gamma ray\nto correlate to porosity. However, if sorting or mineralization are the\ndominant factors in sand porosity variation, then no simple gamma ray\nresponse correlation to porosity should be found because the gamma ray\nresponds to the presence or absence of radioactive minerals. We must\nlearn how the shale is distributed in the sand, for this distribution\ngoverns the productivity.\n\nThere are three broad categories which describe how shale can\nbe distributed in a sand:\n\n## 3. Structural - sand sized shale particles in load-bearing\n\npositions within the rock.\n\n## Of course there can be any combinations of these categories.\n\nThus, to quantitatively determine shale content and distribution we have\ndeveloped a simple mathematical model which relates gamma ray response to\nshale distribution and concentration. The five main assumptions in the\nmodel are the following:\n\n1. There are only two rock types, a high porosity \"clean\" sand\nand a low porosity \"pure\" shale. The observed in situ\nporosities are generated by mixing the two.\n\n## 2. Within the interval investigated, there is no change in shale\n\ntype and the shale mixed in the sand is mineralogically the\nsame as the \"pure\" shale sections above and below the sand.\n\n## 3. The gamma ray responds to the number of radioactive events in\n\na material and thus its mass. The shale fractions we wish to\ndetermine are a function of volume. We assume for the Tertiary\nbasins that both sands and shales have comparable grain\ndensities, thus, the radioactivity will be proportional to\nvolume.\n\n## 4. Constant background radiation will be assumed to be present\n\nin all measurements.\n\n## 5. Counting yields will not change as rock types are intermixed.\n\nThe components of the system are sand and shale, thus, we have\nchosen to use shale rather than clay minerals, even though it is the clay\n\n-2-\nSPWLA SIXTEENTH ANNUAL LOGGING SYMPOSIUM, JUNE 4-7, 1975\n\nwhich contains the bulk of the radioactive material. We believe shaly sands\nand shales are mineralogically similar because both facies are derived from\nthe same source material, carried by the same river and emptied into the\nsame basin. The differentiation between sands and shales begins as the\nparticles settle at differing rates according to their size and transport\nenergy and not mineral type. (This is not rigorously true but, except for\nheavy minerals, very vesicular minerals, or colloids the differences in\ndensity are not dominant.) Thus, we feel the porosity destroying material\nintroduced into a sand stratum will be of the same composition as the\nshales above and below the sand stratum. Of course, this will not be true\nfor the diagenetic alteration of feldspars into clay within the sand\nstratum.\n\n## We define the subscripts a = sand and b = shale. Take a solid\n\nblock of sand material and place it near an instrument capable of measuring\nthe gamma rays emitted, we observe a counting rate, Ra, expressed as\n\nRa* = Ya Aa (1)\nwhere Y is the counting yield, A is the activity and the asterisk indicates\nthat fla= 0.\n\nNow if we crush the solid and build a porous rock with the pieces, we\nintroduce a void space, Ya. Express Va in terms of the fraction of the\ntotal volume of rock, Vt, then V,/Vt = @a, the pure sand rock porosity.\nThe grain volume fraction, grainosity, is then Xa, and Xa = (l-@a). If we\nnow repeat the gamma ray detection experiment using this new porous rock,\nthe counting rate observed is\n\n## R, = (l-@a) Ya' Aa (2)\n\nwhere the prime was added to denote a change in counting yield because of a\ngeometry change in the material counted.\n\n## If we repeat the same crushing and construction experiment using\n\nthe shale material, we observe\n\nRb = (I-&,) Yb ’ fib .\n\nLet's now mix together quantities of the porous sand and shale,\nand assume the counting yield will not be significantly altered (Assumption\nNo. 5). We will elaborate on the error caused by this assumption in\nAppendix 1. There are three independent ways to place the shale in the\nsand block and these are treated separately.\n\n## Place some shale in the sand's pore space. We define the\n\nfraction of the total volume occupied by this shale as Xb.\n\nT\n- 3 -\nSPWLA SIXTEENTH ANNUAL LOGGING SYMPOSIUM, JUNE 4-7, 1975\n\nR=R,+ Xb Rb (5)\n\n## or simply the observed count rate increases proportional to\n\nthe amount of shale added to the pore systems.\n\n## If we are to apply this concept to borehole gamma ray measurements\n\nwe must relate a defined parameter, y, which correlates to porosity, in\nterms Of Xb, the bulk volume fraction occupied by shale.\n\n## The value of y in a sand stratum is defined in terms of the\n\nabove parameters as\n\nRb - R\nY=\nRb - Ra (6)\n\n## where Rb is observed in the \"purest\" nearby shale, and Ra observed in the\n\nnearest \"clean\" sand.\n\n## Substituting (5) into (6), then\n\nRb - (Ra + Xb Rb)\nY= (7)\nRb - Ra\n\n## For simplicity lets define\n\nRb (8)\n' = Rb - Ra\n\nwhich is a measure of how radioactive the sands are. The relation between\ny and Xb then becomes\n\nxb = l-y\n5\nwhen Xb is pore filling.\n\n## One point to note is that the minimum porosity available to the\n\ndispersed model is when shale completely fills all the original pore\nvolume of the sand or when\n\nXb = @a,\n\n## 0 min, dispersed = 0, x @b. (10)\n\n- 4 -\nSPWLA SIXTEENTH ANNUAL LOGGING SYMPOSIUM, JUNE 4-7, 1975\n\nWhen Xb > fla, then equation (4) for the counting rate is not valid because\nwe must remove sand grains to add shale. We derive this equation by\nstarting with pure shale (Xb = 1) and work back to Xb = @a. Thus, R =\n(1-0b) Yb'Ab - Xa (l-@b) Yb'Ab + Xa (I-8a) Ya'Aa. (11)\n\n## Substituting (2) and (3) into (11) we get\n\nR = Rb - XaRb + XaRa. (12)\nUsing Xa = 1-Xb, (12) rearranges to R = Rb - (1-Xb)(Rb-Ra)' (13)\n\n## Substituting (13) into (6), y = 1-Xb = Xa . (14)\n\n2. Laminated model\n\nNow when we add shale to the sand stratum we must replace sand\nand its associated porosity, fla,with shale to keep a constant\ntotal volume of material. The amount of sand removed and shale\nadded is Xb, the sand fraction. Thus\n\n## Substituting (2) and (3) into (15) yields\n\nR = Ra + Xb (Rb-Ra)* (16)\n\nRb - Ra\n\n3. Structural\n\n## When we add shale in structural positions we remove sand grains\n\nonly. Thus the porosity increases with the amount of shale\nporosity that we add in place of the solid sand grain. Or\n\n## which is the same as (15). Thus, the y to Xb relationship for\n\nstructural shale is identical to that for the laminated model.\n\nT\n-5-\nSPWLA SIXTEENTH ANNUAL LOGGING SYMPOSIUM, JUNE 4-7, 1975\n\n## Now that we know the relation between y and shale fraction, we\n\ncan construct a theoretical y-porosity relationship based on these three\nmodels.\n\n## 1. Dispersed (pore filling) - we start with the total porosity\n\nof a or @a. We then add shale in the pore space, thus\ndecreasing the porosity by the amount of grainosity of the\nshale.\n\n## 0dis = @a - xb (1-gb) for Xb < @a, the available space (19)\n\nfor shale.\n\nThe end points of this equation are easily fixed and are\nindependent of any proposed relation between Xb and y.\nWhen Xb = 0, 0&& = 8a and when Xb = 8a, @&a = 0a@b.\n\n## 0dj.s = @a- (1-Y) (l-f&).\n\n5 (20)\nA reasonable number for 5 in South Louisiana sands is 1.25.h\nThus the relation between these end points is linear with y.\nThe actual value of y at 0~1~ is difficult to define\nabsolutely because of Assumption No. 5. The error caused\nby this assumption is discussed in Appendix 1. The porosity\nrelation for the region when Xb > 0, is derived just as is\nthe radiation relationship by starting with pure shale and\nadding sand grains which have no porosity, thus reducing\nthe total porosity by the value of sand added.\n\nwhen Xb > fla.\n\n## Q)dis = @b-Ylbb. The relation is linear with y. (22)\n\nWhen y = 0, 0dis = 0b and this is a fixed end point.\nymax in eq. (22) is limited as Ymin in eq. (20). However\nthis number is difficult to fix as stated before. See\nAppendix 1.\n\n## 2. Laminated - in this case we remove both the porosity and\n\ngrainosity of the sand and replace it by the shale porosity\nand grainosity.\n\n*This value is derived from eq. (8) using Rb = 100 API units and Ra = 20 API units.\n\n- 6 -\nSPWLA SIXTEENTH ANNUAL LOGGING SYMPOSIUM, JUNE 4-7, 1975\n\n## ham = 0a - xb (8,) + xb (0b). (23)\n\nSubstitute (17) into (23)\n\n## O1am = Y@a + (1-Y) 0b- (24)\n\nThe end points are easily fixed when y = 1, @lam T 0, and\nwhen y = 0, @Iam x P)b. These end points are independent\nof y-xb relation and are firm. Also equation (24) demonstrates\na linear relation between the two end points.\n\n## 3. Structural - in this case we remove no sand porosity, only\n\nsand grainosity, and replace it with an equivalent bulk volume\nfraction of shale porosity.\n\n## The maximum amount of structural shale which can be added\n\nequals the grainosity of the sand or Xmax = l_Ymin = l-P)a. (27)\n\n## Notice that 0 increases linearly with decreasing y. This\n\nstartling result is obvious upon inspection of the model and\nis the consequence of replacing the solid quartz grain with a\ncorresponding volume of porous shale. The radiation at the\nmaximum is a simple relation because no sand grains remain.\nHowever, the counting yield will be different than for pure\nshale. But if we use Assumption No. 5, then\n\n## Then substituting (28) into (6)\n\nRb - (1-qa)Rb = Rb (@a)\nY\" (29)\nRb-Ra Rb - R,.\n\n## Substituting (8) into (29)\n\nY = 5 (0,) * (30)\n\nThus (27) and (30) are not equal, again the consequences of\nAssumption No. 5. See Appendix 1.\n\nT\n- 7 -\nSPWLA SIXTEENTH ANNUAL LOGGING SYMPOSIUM, JUNE 4-7, 1975\n\n## In reality we do not have any of these pure models but rather\n\nwe have a combination of the three. One simplification is to assume the\namount of structural shale is too small to be significant and remove this\npossibility from the model. This simplification permits the response of\na gamma ray-density log to be solved (graphically or algebraically) for\nsand fraction, sand porosity and shale distribution.\n\n## As an example we choose a Miocene reservoir in South Louisiana,\n\nwhere clean sand porosity is 33% and pure shale porosity is 15%. This is\nthe same reservoir shown in Figure 1. We can then construct a y-density\nporosity crossplot triangle limited by these data, using eq.(20), (22),\nand(24), shown in Figure 2. Eq. (26) is also presented.\n\n## This is done by fixing the y = 1 point at 8 = 33%, y = 0 at 15%.\n\nA line drawn between these points is the laminated model limit expressed\nby eq. 24. The minimum flfor the dispersed is given by eq. 10 as 8, x @b\nor 0.0495. Solution of eq. 20 for y, using 5 = 1.25, yields y = 0.588.\nA line connecting this point to the y = 1 point is the graphical approxi-\nmation of eq. 22.\n\n## Isolaminous lines are added to Figure 2 by constructing lines\n\nparallel to the dispersed shale model line. The percent laminations is\nthen read from the laminated model line as the percentage of the laminated\nmodel line substended by the isolaminous line measured from the y = 1.0\napex. Isoporous lines are added to Figure 2 by constructing lines which\nconnect the y = 0 apex to the dispersed shale model line. The porosity\nof the sand laminae anywhere along a given line is read at its intercept\non the dispersed shale model line. For a specific example, a FDC log in\na thick sand reads 0 = 28% and y = 0.85. Using Figure 2, we start at the\no- 28, y = .85 point, which is on an isolam corresponding to 10% shale\nlaminations, then proceed up an isopor to the intercept on the dispersed\nshale model line of Id= 29.4. Thus, for this example the bed is composed\nof 10% shale laminations and the porosity of the interbedded sand is 29.4%.\nWe have illustrated this solution graphically, but of course it can be\ndone algebraically.\n\n## We recently had the opportunity to test this hypothesis when\n\nwe cored a well in South Louisiana which penetrated this same reservoir.\nFigure 3 shows the petrophysical log section across the reservoir.\nFigure 4 shows the oil saturation and porosity calculated for the entire\ninterval. Figure 5 shows some of the core photographs, demonstrating the\nlaminated nature of the sand. Note the good sand at the top and the\nextremely laminated material at the bottom. Figure 6 shows the correspond-\ning FDC 8 plotted versus stressed core porosity. The FDC 8 is calculated\nusing measured grain densities and fluid densities from the core adjusted\nto reservoir temperature and pressure. The good agreement in the clean\nsand is apparent, while a corresponding disparity appears in the lower\nlaminated section. This is an artifact of biased sampling. Only the sand\nbetween the laminations was plugged for core analysis, thus giving mis-\n\n- 8 -\nSPWLA SIXTEENTH ANNUAL LOGGING SYMPOSIUM, JUNE 4-7, 1975\n\nUsing the core photographs, the amount of sand and shale can\nbe counted precisely and when a clean sand porosity of 31% (the average\n0 from stressed core analysis) and pure shale porosity of 15% are\nassigned to the laminations, the average porosity as seen by the density\nlog is reproduced. Conversely, from the gamma ray-density log porosity\ncrossplot, the sand fraction and sand porosity matches that counted from\nthe photographs and measurements in the lab.\n\n## Thus, if one knows he is in a laminated environment he can\n\napply the laminated resistivity model;\n\n1 fsd b\n-Ra = R,d x R,h\n\nThe value of R, is read from the induction log, f,d and fsh are\nobtained from the crossplot, and Rsh takes from the induction log in a\nnearby shale zone. Then the actual value percent of Rsd and Rt of the\nsand can be calculated. The effect of using the true sand 0 and Rt to\ncalculate So is shown in Figure 7. This is a repeat of Figure 4, with\nan overlay showing the change in calculated So in the heavily laminated\nzones. In most cases, the oil saturation increases. The effect shown\nhere increases as the percent laminations increase to the point where\nthe shale resistivity dominates the apparent resistivity, thereby\ncondemning a zone which could produce hydrocarbons.\n\nACKNOWLEDGMENT\n\n## The authors wish to thank Shell Oil Company for granting\n\npermission to publish this work. We also thank B. E. Ausburn of Shell\nOil Company who allowed us to use Figure 4 which he had prepared earlier.\nWe appreciate the many discussions with our collegues who helped solidify\nmany of the concepts presented.\n\nSYMBOLS\n\nY- void space\n\n## Y- counting yield, an experimental constant which relates the true activity\n\nto the number of events counted by the detector\n\n## a - subscript for clean sand\n\nT\n- 9 -\nSPWLA SIXTEENTH ANNUAL LOGGING SYMPOSIUM, JUNE 4-7, 1975\n\n## f- fraction of bulk volume, used in Resistivity models\n\nY- defined by eq. 6 using counting rates in pure shales and clean sands.\nIt is often the sand fraction.\n\n## 0- porosity, the void space of a rock expressed as a volume fraction\n\nof the total bulk volume.\n\n## X- grainosity, the solid.part of a rock expressed as a volume fraction\n\nof the total bulk volume.\n\nAPPENDIX1\n\n## We realize that errors have been introduced to the model by\n\nmany of our assumptions. However, these assumptions are necessary to\narrive at the simple equations presented in the text. We feel justified\nin using assumption (5) because we are also assuming no fluid radio-\nactivity and constant background in spite of unknown changes in borehole\nsize and rugosity, cement type. and placement, and detector type and size.\n\n## By assigning a few numbers to the equations we can explore the\n\npotential errors caused by assumption (5) and demonstrate the small error\nintroduced by its acceptance.\n\n## Let's refer to Figure 2. The y = 1 point is fixed by the\n\nuncertainty in determining 0a from field measurements. But for the\ntheoretical model we can set this number exactly, thus the y = 1, 0 = @a\napex is firm. Similarly for the y = 0, 8 = t\\$, apex. Equation (24)\ndemonstrated that the equation which connects these two apexes is linear,\nthus the posi ion of this line is firm within the confines of the other\nassumptions. The minimum 0 available is fixed at @a&. However, the\nvalue of y at this point is less well known. Eq. (20) predicts y = -59\nwhile Eq. (22 predicts y = .67. The actual value is probably between t ne\ntwo, thus the max error for fldis in the working area of the triangle\n(8 apparent > @b) is -\n+1.5 and the mean error about -+.5. We feel this is\nacceptable for any practical application. For the structural shale model\nwe have similar uncertainties in y at the @max point. The value of @max\niS fixed at 8a + Xa@b or 0a + (l-oa) fib = .43. We can calculate y = .33\nfrom eq. (27) and y = .41 from eq. (30). The Ib error introduced by\nuncertainty in y is less than -\n+.5.\n\n- 10 -\nSPWLA SIXTEENTH ANNUAL LOGGING SYMPOSIUM, JUNE 4-7, 1975\nI\nY '0\n- 12 -\nAPI UNITS\n0 60\nI I\n\n## 011 SATURATION, FRAC. PV POROSITY. FRAC. BV\n\n0 jo . 20 -30 .40 .50 .60 .?O .32 .30 .2B .2b .24 .22 20\nI I I I I I I I I I I I I I 1\n2\n0\n0\n\nI I\n.z\n\ni -\n\nI\n%\nrl\n\n87950-\n_J\nI\nI I\n\nBoo0 -\n,,.,S.,t\n5 +\n\nDENSITY LOGS.\n\nmv ohm-meters\n\n## FIGURE 3 PETROPHYSICAL SECTION FOR RESERVOIR IN SOUTH LOUISIANA,\n\nCORED INTERVAL SHOWN BY BAR IN TRACK I.\nOIL SATURATION, FRAC PV POROSITY, FRAC BV\n0 .lO .20 .30 .40 .M .6O .70 .80 34 .32 .30 .28 .26 .24\nI I I 1 I I 1 I I\n-----I r ----,-\n\n_-_...a\n1\nr.___-\n7900 -\n\nl-------\nl\nI\nI\nI\nr___*____-_\nI\n\nJ-\nL__\n:----\n\n!I\nL__.-_\n\n## FIGURE 7 OIL SATURATION-POROSITY PROFILE FROM DEEP INDUCTION AND\n\nDENSITY LOGS, SOLID LINE. CORRECTED FOR SHALY SAND EFFECTS\nON INDUCTION & DENSITY SHOWN DOTTED LINE.\n\n## FIGURE 6 FDC POROSITY & STRESSED CORE POROSITY DEMONSTRATING APPARENl\n\nDISCREPANCY BETWEEN ANALYSIS METHODS CAUSED BY LAMINATIONS." ]

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[ "# Work and electric potential energy of a capacitor\n\n## Homework Statement\n\nThere's no problem per se, I'm just confused by the definition of work and electric potential energy: work done by the electric field is defined to be the negative of delta_U, the change in electric potential energy. This definition makes sense to me.\n\nHowever, according to my textbook, it is the other way round for capacitors: the total work to charge a capacitor is defined as Q^2 / (2C), which according to my textbook is the same as the electric potential energy U of the charged capacitor. Where did the minus sign go?\n\n## Homework Equations\n\nW(done by electric field) = - delta_U\n\nQ^2 / (2C) = W = U\n\nThanks.\n\nDelphi51\nHomework Helper\nI don't really see the conflict. In the first case, the electric field does work on something so the field or whatever is maintaining it loses energy, its ΔU is negative, so you need -ΔU to get a positive value for the work done to a charge.\n\nIn the second case, a battery does work to charge a capacitor. The battery loses energy and has a negative ΔUb = -QV, while the capacitor gains energy and has a positive ΔUc = Q²/(2C).\n\nNow I'm wondering if ΔUc = -ΔUb. Yikes; I may lose sleep over this!\nThe factor of 2 must come into it due to the battery with voltage V pouring charge into a capacitor while its voltage rises from zero to V, average V/2. Half the energy is lost . . . in the wire?\n\nehild\nHomework Helper\nThe battery has got stored chemical energy and this decreases when the buttery supplies charges to the capacitor. Some chemical reactions occur inside the battery, metal ions go into the electrolyte from one of the electrodes and hydrogen evolves on the other one. This process sooner or later makes the battery flat. During the process, also some heat evolves. So the energy loss comes partly because of the change of chemical energy in the battery and also because of the evolved heat.\n\nehild" ]

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[ "# Example 5: Dense Data¶\n\nThe FleCSI data model provides several different storage types. A storage type is a formal term that implies a particular logical layout to the data of types registered under it. The logical layout of the data provides the user with an interface that is consistent with a particular view of the data. In this example, we focus on the dense storage type.\n\nLogically, dense data may be represented as a contiguous array, with indexed access to its elements. The dense storage type interface is similar to a C array or std::vector, with element access provided through the () operator, i.e., if var has been registered as a dense data type, it may be accessed like: var(0), var(1), etc.\n\nIn the fields example (04-fields), we were actually using the dense storage type to represent an array of double defined on the cells of our specialization mesh. This example is an extension that demonstrates using user-defined types as dense field data.\n\nThis example uses a user-defined struct as the dense data type. The struct_type_t is defined in the types.h file:\n\n```#pragma once\n\n#include <flecsi/data/dense_accessor.h>\n\nnamespace types {\n\nusing namespace flecsi;\n\n// This is the definition of the struct_type_t type.\n\nstruct struct_type_t {\ndouble a;\nsize_t b;\ndouble v;\n}; // struct_type_t\n\n// Here, we define an accessor type to use in the task signatures in our\n// example. Notice that the base type \"dense_accessor\" takes four\n// parameters. The first parameter is the type that has been registered on\n// the associated index space. The other three parameters specify the\n// privileges with which the corresponding data will be accessed.\n\ntemplate<\nsize_t SHARED_PRIVILEGES>\nusing struct_field = dense_accessor<struct_type_t, rw, SHARED_PRIVILEGES, ro>;\n\n} // namespace types\n```\n\nAside from using a struct type, this example of registering data is identical to registering a fundamental type, e.g., double or size_t.\n\nThe code for this example can be found in dense.cc:\n\n```#include <iostream>\n\n#include<flecsi/tutorial/specialization/mesh/mesh.h>\n#include<flecsi/data/data.h>\n#include<flecsi/execution/execution.h>\n\n#include \"types.h\"\n\nusing namespace flecsi;\nusing namespace flecsi::tutorial;\nusing namespace types;\n\nflecsi_register_data_client(mesh_t, clients, mesh);\nflecsi_register_field(mesh_t, types, f, struct_type_t, dense, 1, cells);\n\nnamespace example {\n\n// This task initializes the field of struct_type_t data. Notice that\n// nothing has changed about the iteration logic over the mesh. The only\n// difference is that now the dereferenced values are struct instances.\n\nvoid initialize_field(mesh<ro> mesh, struct_field<rw> f) {\nfor(auto c: mesh.cells(owned)) {\nf(c).a = double(c->id())*1000.0;\nf(c).b = c->id();\nf(c).v = double(c->id());\nf(c).v = double(c->id())+1.0;\nf(c).v = double(c->id())+2.0;\n} // for\n} // initialize_field\n\nflecsi_register_task(initialize_field, example, loc, single);\n\n// This task prints the struct values.\n\nvoid print_field(mesh<ro> mesh, struct_field<ro> f) {\nfor(auto c: mesh.cells(owned)) {\nstd::cout << \"cell id: \" << c->id() << \" has value: \" << std::endl;\nstd::cout << \"\\ta: \" << f(c).a << std::endl;\nstd::cout << \"\\tb: \" << f(c).b << std::endl;\nstd::cout << \"\\tv: \" << f(c).v << std::endl;\nstd::cout << \"\\tv: \" << f(c).v << std::endl;\nstd::cout << \"\\tv: \" << f(c).v << std::endl;\n} // for\n} // print_field\n\nflecsi_register_task(print_field, example, loc, single);\n\n} // namespace example\n\nnamespace flecsi {\nnamespace execution {\n\nvoid driver(int argc, char ** argv) {\n\nauto m = flecsi_get_client_handle(mesh_t, clients, mesh);\n\n// The interface for retrieving a data handle now uses the\n// struct_type_t type.\n\nauto f = flecsi_get_handle(m, types, f, struct_type_t, dense, 0);\n\nflecsi_execute_task(initialize_field, example, single, m, f);\nflecsi_execute_task(print_field, example, single, m, f);\n\n} // driver\n\n} // namespace execution\n} // namespace flecsi\n```" ]

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[ "", null, "Version:\n\nThis documentation is not for the latest stable Salvus version.", null, "This tutorial is presented as Python code running inside a Jupyter Notebook, the recommended way to use Salvus. To run it yourself you can copy/type each individual cell or directly download the full notebook, including all required files.", null, "# Custom Source Time Functions\n\nCopy\n%matplotlib inline\n%config Completer.use_jedi = False\n# Standard Python packages\nimport pathlib\n\n# Third-party imports.\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport pyasdf\n\n# Salvus packages\nimport salvus_flow.api\nimport salvus_flow.simple_config as sc\nfrom salvus_mesh.simple_mesh import basic_mesh\n\n## Main message\n\nSalvus offers a number of parameterized source time functions (STFs) - if that is not sufficient one can construct a custom one from a numpy array as illustrated in the following cell. Several rules apply:\n\n• The array has to have the shape [npts, N] where npts the number of samples and N is the number of source components. The order can also be reversed in which case the array will automatically be transposed by SalvusFlow before the simulations are run.\n• The spatial weights (f[_x, ...], m_[xx, yy, ...]) are always multiplied on top of the given STFs. Thus either normalize these or set the weights all to 1.0.\n• For sources that have multiple components, e.g. vectorial or moment tensor sources, N is either equal to the number of independent source components (xy[z] in the vectorial case, m_xx, m_yy, ... in the tensor case) or equal to 1 in which case a copy of that array will be created before the weights are applied.\n• The order of the given components must either be xy[z] in the vectorial case or adhering to the Voigt notation in the tensor case.\n• Potentially specified rotation matrizes for the sources are applied after the weights and original STFs have been multiplied.\n# A single array.\nstf = sc.stf.Custom.from_array(\nnp.sin(np.linspace(0, 4 * np.pi, 100)),\nsampling_rate_in_hertz=2.0,\nstart_time_in_seconds=0.0,\n)\nstf.plot()\n\n# Combine with a source object to create a complete source object.\n# Note the different weights will define the final source together\n# with the STF.\nsrc = sc.source.cartesian.VectorPoint2D(\nx=10.0, y=0.0, fx=1e-2, fy=-2e-2, source_time_function=stf\n)", null, "# It is also possible to specify a separate array for every components.\narray = np.array(\n[\n1.5 * np.sin(np.linspace(0, 4 * np.pi, 100)),\n-3.0 * np.sin(np.linspace(0, 4 * np.pi, 100)),\n]\n)\n\nstf = sc.stf.Custom.from_array(\narray, sampling_rate_in_hertz=2.0, start_time_in_seconds=-10.0\n)\nstf.plot()\n\n# Note that in this case the weights should be set to 1.0\nsrc = sc.source.cartesian.VectorPoint2D(\nx=10.0, y=0.0, fx=1.0, fy=1.0, source_time_function=stf\n)", null, "## Expanded tutorial\n\n### Introduction\n\nSalvus comes with a few wavelets that can readily be used as source time functions. However, sometimes it is necessary to define a custom source time function. This tutorial shows how to do that.\n\n### Ricker wavelet as custom source time function\n\nThe Ricker wavelet is the second derivative of a Gaussian, and defined as\n\n$s(t) = \\left(1 - 2\\,t^2\\,\\pi^2\\,\\omega^2\\right) \\, \\exp\\left(-t^2\\,\\pi^2\\,\\omega^2\\right),$\n\nwhere $t$ is the time and $\\omega$ is the center frequency.\n\nTo see the connection with a Gaussian, it helps to define\n\n$\\sigma = \\left(\\pi\\,\\omega\\right)^{-1},$\n\nwhich gives\n\n$s(t) = \\left(1 - \\frac{2\\,t^2}{\\sigma^2}\\right) \\, \\exp\\left(-\\frac{t^2}{\\sigma^2}\\right).$\n\n$s(t)$ is centered around zero, so we either have to introduce a time shift, or start the simulation at a time $t < 0$.\n\nThere are two important things to notice:\n\n• To avoid artifacts in the wavefield the custom source function should always start smoothly from zero to be compatible with the homogeneous initial conditions.\n• You don't need to worry too much about the correct sampling rate, as the source time function will be resampled internally using the actual time step of the simulation. Just make sure that you have sufficiently many data points to avoid undersampling.\nwavelet_width_in_seconds = 0.1075\ntime_step_in_seconds = 1e-3\ncenter_frequency = 14.5\n\nsigma_2 = 1 / (np.pi * center_frequency) ** 2\n\ntime = np.linspace(\n-wavelet_width_in_seconds,\nwavelet_width_in_seconds,\nint((2 * wavelet_width_in_seconds / time_step_in_seconds)),\n)\n\nsampling_rate_in_hertz = 1.0 / time_step_in_seconds\n\nwavelet = (1 - (2 * time ** 2) / sigma_2) * np.exp(-(time ** 2) / sigma_2)\n\n# plot the wavelet\nplt.plot(time, wavelet)\nplt.xlabel(\"time [s]\")\nplt.ylabel(\"amplitude\")\nplt.title(\"Custom ricker wavelet\")\nplt.show()", null, "### Simulation setup\n\nTo run a simulation with our custom source time functions, we'll just use a very simple example mesh.\n\n# Simple 2D elastic mesh.\nmesh = basic_mesh.CartesianHomogeneousIsotropicElastic2D(\nvp=3200.0,\nvs=1847.5,\nrho=2200.0,\nx_max=2000.0,\ny_max=1000.0,\nmax_frequency=25.0,\n).create_mesh()\n\nreceiver = sc.receiver.cartesian.Point2D(\nx=1400.0, y=700.0, station_code=\"XX\", fields=[\"displacement\"]\n)\n\nNow we'll demonstrate the creation of the same source plus source time function in three different ways:\n\n1. Using a built-in parameterized source time function.\n2. Using a single component custom source time function and corresponding weights.\n3. Using a multi-component source time function.\n# Spatial weights of the vectorial source.\nfx = 1e-5\nfy = -0.8e-4\n\n# Location.\nsx = 1000.0\nsy = 500.0\n\n# Option 1 - Parameterized STF.\nstf_1 = sc.stf.Ricker(center_frequency=14.5)\nsource_1 = custom_source = sc.source.cartesian.VectorPoint2D(\nx=sx, y=sy, fx=fx, fy=fy, source_time_function=stf_1\n)\n\n# Option 2 - single-component STF and associated weights.\nstf_2 = sc.stf.Custom.from_array(\narray=wavelet,\nsampling_rate_in_hertz=sampling_rate_in_hertz,\nstart_time_in_seconds=time,\n)\nsource_2 = sc.source.cartesian.VectorPoint2D(\nx=sx, y=sy, fx=fx, fy=fy, source_time_function=stf_2\n)\n\n# Option 3 - multi-component STF and unit weights.\nsource_time_function = [wavelet * fx, wavelet * fy]\nstf_3 = sc.stf.Custom.from_array(\narray=source_time_function,\nsampling_rate_in_hertz=sampling_rate_in_hertz,\nstart_time_in_seconds=time,\n)\nsource_3 = sc.source.cartesian.VectorPoint2D(\nx=sx, y=sy, fx=1.0, fy=1.0, source_time_function=stf_3\n)\nstf_1.plot()\nstf_2.plot()\nstf_3.plot()", null, "", null, "", null, "Now it is time to actually run the simulations.\n\nfor _i, src in enumerate([source_1, source_2, source_3]):\nsim.physics.wave_equation.end_time_in_seconds = 0.5\n\nsalvus_flow.api.run(\nsite_name=\"local\",\ninput_file=sim,\nranks=1,\noutput_folder=f\"output_custom_{_i}\",\noverwrite=True,\n)\nJob job_2004152235946279_0948a8adeb running on local with 1 rank(s).\nSite information:\n* Salvus version: 0.10.12\n* Floating point size: 32\n\n\n* Downloaded 17.8 KB of results to output_custom_0.\n* Total run time: 2.26 seconds.\n* Pure simulation time: 1.70 seconds.\nJob job_2004152235157469_74895e17b1 running on local with 1 rank(s).\nSite information:\n* Salvus version: 0.10.12\n* Floating point size: 32\n\n* Downloaded 18.0 KB of results to output_custom_1.\n* Total run time: 8.12 seconds.\n* Pure simulation time: 4.10 seconds.\nJob job_2004152236296055_f2543d2b14 running on local with 1 rank(s).\nSite information:\n* Salvus version: 0.10.12\n* Floating point size: 32\n\n* Downloaded 17.9 KB of results to output_custom_2.\n* Total run time: 7.25 seconds.\n* Pure simulation time: 6.68 seconds.\n\n\n### Compare results\n\n_, axes = plt.subplots(nrows=1, ncols=2, figsize=(15, 5))\n\nfor _i in range(3):\nfolder = pathlib.Path(f\"output_custom_{_i}\")\nwith pyasdf.ASDFDataSet(folder / \"receivers.h5\") as ds:\nfor _j, ax in enumerate(axes):\ntr = ds.waveforms.XX_XX.displacement[_j]\nax.plot(tr.times(), tr.data, label=f\"Source {_i}\")\nax.set_title(f\"Component {_j + 1}\")\naxes.legend()\naxes.legend()\nplt.show()", null, "As expected the traces look exactly the same. If you modify any of the parameters of any of the three sources you will see a difference.", null, "PAGE CONTENTS" ]

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null, 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 ", null, 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 ", null, 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 ", null, 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 ", null, 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 ", null, 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null ]