3)The file Description.pdf, which explains how to use the functions and gives a short overview of the algorithms. https://in.mathworks.com/matlabcentral/fileexchange/1480-sensitivity-analysis-for-odes-and-daes. Retrieved November 4, 2022. Thus MATLAB's ODE solver suite can become more efficient by using methods which reduce the number of function calls (which multistep methods do). the sensitivity of the ith independent variable to the jth parameter is $\frac{\partial y}{\partial p_{j}}$. MATLODE implements two distinct approaches for sensitivity analysis: direct (via the tangent linear model) and adjoint. Global Sensitivity Analysis (GSA) is a term describing a set of mathematical techniques to investigate how the variation in the output of a numerical model can be attributed to variations of its inputs. Jupyter Notebook. I have seen this question asked a lot and I am clear why it cannot be done. The display follows the column order shown in names for Accelerating the pace of engineering and science. Sensitivity analysis of odes . Define the Experiments (Signal Matching Requirements) - Definition of the measured and expected signal data to use for signal matching requirements. (ODE) simulations. 2. where n is the number of steps taken by the ode You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. Accepted Answer Jan on 18 Jul 2021 1 Link Sensitivity means, that you vary the initial values or parameters by a small value and compare the results of the integration. Download and share free MATLAB code, including functions, models, apps, support packages and toolboxes Create scripts with code, output, and formatted text in a single executable document. Reload the page to see its updated state. The implemented controller in e.g. set to true at any given time. For smooth functions the resulting matrices are identical in first order. summarized in Property Summary. The methods can answer substantially different results, if there are poles or discontinuities near to the trajectory. Bilal used Sobol's method of global sensitivity analysis to calculate the first order your location, we recommend that you select: . The MATLAB's ode23s function is used to integrate differential equations of the mPBPK models. Sensitivity Analysis for ODEs and DAEs (https://www.mathworks.com/matlabcentral/fileexchange/1480-sensitivity-analysis-for-odes-and-daes), MATLAB Central File Exchange. respect to the input factors. The settling model parameters were also considered. Only one configuration set object in the model object can have the Active property Sensitivity Analysis. The methods can answer substantially different results, if there are poles or discontinuities near to the trajectory. The most widely used are AUTO86/97 [1], CONTENT [2] and XPPAUT.The Matlab software package . Since x and y are INFORM=1. Reload the page to see its updated state. ntrp15s.m, odezero.m, icdae.m, icsdae.m. Is there any other toolbox available in MATLAB for performing sensitivity analysis of odes? 1. Numerical Integration and Differential Equations, You may receive emails, depending on your. In the Sensitivity Analyzer, click Open Session and Open from model workspace. The parameter sensitivities for ASM1 and ASM3 were analyzed by three techniques such as SVM-Slope, RVM-SlopeMA, and RVM-AreaCRF. Accelerating the pace of engineering and science. This anonymous function is called by sdo.evaluate at each iteration of the evaluation problem to evaluate the model at all combinations of parameters. offers. MATLAB's ODE solver requires taking in a user-defined function, and since this function is defined in MATLAB its function calls are very inefficient and expensive. Sensitivity analysis lets you explore the effects of variations in model quantities (species, compartments, and parameters) on a model response. 2) Four MATLAB 5.3 files which are not in Matlab R 6.1 and may be called from SENS_SYS and SENS_IND: ntrp15s.m, odezero.m, icdae.m, icsdae.m. Choose a web site to get translated content where available and see local events and offers. Learn more about sensitivity analysis, ode MATLAB An analysis of the sensitivity can be achieve by two methods: . We are now in a position to compute the sensitivities of the individual eigenvalues. Different mathematical calculation methods can be divided into: trajectory sensitivity method [17], output sensitivity method [18], matrix sensitivity method [19], global sensitivity method [20 . From the Evaluate Model list, select Generate MATLAB Function. The code I used to get the solution for the model . To enable or disable sensitivity analysis, use the SensitivityAnalysis property. Open session sdoVOR_sasessionForEvaluation. You use the Sensitivity Analyzer to define an evaluation problem for a model of the body's vestibulo-ocular reflex, and generate MATLAB code to solve this evaluation problem. Recently sensitivity analysis methods are also becoming increasingly popular in the area of compressor simulation models and many new sensitivity analysis techniques have been developed lately Bilal (2011) and (Bilal, et al., 2006). Modify the generated sensitivityEvaluationSdoVOR function to include or exclude new experiments or other requirements, or change evaluation options. 12 PDF Solving Ordinary Differential Equations I: Nonstiff Problems E. Hairer, S. P. Nrsett, G. Wanner Economics 1993 Unable to complete the action because of changes made to the page. Sensitivity analysis provides a cheap way to calculate the gradient of the solution which can be used in parameter estimation and other optimization tasks. Very little seems to have developed in the interim. First, I am not trying to parallelize ode45 (or any other solver). The system has a lot of parameters and I'd like to perform sensitivity analysis. SENS_IND and SENS_SYS use different algorithms for the same task (see the Description.pdf file for small overview). So I want to do a parameter sensitivity analysis to justify the values of the parameters that can give me a valid solution (positive solution). Web browsers do not support MATLAB commands. The adjoint solvers support gradient calculation for multiple cost functions, and the tangent linear solvers support gradient calculation with respect . Learn more about sensitivity analysis The methods can answer substantially different results, if there are poles or discontinuities near to the trajectory. Choose a web site to get translated content where available and see local events and Sensitivity Analysis for ODE and DAE Manual Pages. the values in x. 2) Four MATLAB 5.3 files which are not in Matlab R 6.1 and may be called from SENS_SYS and SENS_IND: The idea is new to me and I need some help to give me some hints. I suggest exploring beyond Mathworks for this area of research. (The MATLAB output is fairly long, so I've omitted it here.) They also calculate the correspondent sample-based correlation coefficient (CC_PLOT, RCC_PLOT and PRCC_PLOT, see Table 1 for details). Victor M. Garcia Molla (2022). sites are not optimized for visits from your location. offers. When sensitivity analysis is enabled, the following command. the model object with the addconfigset method. The methods can answer substantially different results, if there are poles or discontinuities near to the trajectory. and display. Choose a web site to get translated content where available and see local events and Read 4 answers by scientists to the question asked by Mahdi Alibeigi on Nov 28, 2020 You can add a number of configuration set objects with different SensitivityAnalysisOptions to For smooth functions the resulting matrices are identical in first order. In this example we load a pre-configured Sensitivity Analyzer session based on that example. MATLAB 6.*. Please, e-mail us if you have any comment or find problems. I have struggled to find anything for this kind of sensitivity analysis using Matlab over the years. This example shows how to automatically generate a MATLAB function to solve a Sensitivity Analysis evaluation problem. Updated on Aug 15. Old versions of the odeset.m and odeget.m functions have been included in the zip file, because in recent Matlab versions these functions have been changed, and do not work properly with sens_sys.m and sens_ind.m, Two bugs corrected, related to handling of init files. Fed-batch Reactor Optimal Parametric Sensitivity Control . You'll discover: The differences between local and global sensitivity analysis and when it is appropriate to apply each method. This opens a preconfigured session in the Sensitivity Analyzer. Use Sensitivity Analysis to evaluate how the parameters and states of a Simulink model influence the model output or model design requirements. You can use the analysis to validate preexisting knowledge or assumption about influential model quantities on a model response or to find such quantities. See Description for more information. For global sensitivity analysis, you will want to do a monte carlo simulation, which will be more computationally intensive. This opens a preconfigured session in the Sensitivity Analyzer. Open session sdoVOR_sasessionForSensitivityStatistics. You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location. your location, we recommend that you select: . Analyze cost function sensitivity to model parameters using design of experiments (DOE), Monte Carlo, and correlation techniques. Call the generated sensitivityEvaluationSdoVOR function with a different set of parameter values to evaluate. Import the radio decay model from SimBiology demos. offers. The generated code is added to the MATLAB editor as an unsaved MATLAB function. For smooth functions the resulting matrices are identical in first order. MathWorks is the leading developer of mathematical computing software for engineers and scientists. The local sensitivity of the solution to a parameter is defined by how much the solution would change by changes in the parameter, i.e. Based on Generate MATLAB Code for Sensitivity Analysis for Design Space Exploration and Evaluation (GUI) This example shows how to automatically generate a MATLAB function to solve a Sensitivity Analysis evaluation problem. Fortran. MathWorks is the leading developer of mathematical computing software for engineers and scientists. You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. The function you link to doesn't allow for passing additional arguments to odefun so was rather limited when I encountered it around 5 years ago. MathWorks is the leading developer of mathematical computing software for engineers and scientists. Local forward sensitivity analysis directly gives the gradient of the solution with respect to each parameter along the time series. Generate MATLAB Code From the Compute Statistics list, select Generate MATLAB Function. This paper describes the implementation aspects of FATODE, code organization and usage aspects, and demonstrates a simple example of its application on a small chemical mechanism for both ODE integration and sensitivity analysis. Modify the integrator internally: In each step of the solver create the matrix by the numerical differentiation. I The picture is then linear transformed (sheared) and shown on the right. A collection of general Fortran modules in the categories Computational, Date and Time, Input / Output, Math / Numerics, Screening, Sensitivity Analysis and Optimising / Fitting, and Miscellaneous. For details on how to write an objective/constraint function to use with the sdo.evaluate command, type help sdoExampleCostFunction at the MATLAB command prompt. This opens a preconfigured session in the Sensitivity Analyzer. Analysis of ODE models Some Concepts Eigenvalue and Eigenvector with Mona Lisa I In the left picture, two vectors were drawn on the Mona Lisa. Learn about the Global Sensitivity Analysis (GSA) functionality in SimBiology . Sensitivity coefficients with respect to all rate constants and initial conditions are computed successfully using our algorithm with a tolerance of 10 -9. https://www.mathworks.com/matlabcentral/answers/439874-sensitivity-analysis-of-an-ode, https://www.mathworks.com/matlabcentral/answers/439874-sensitivity-analysis-of-an-ode#comment_660686, https://www.mathworks.com/matlabcentral/answers/439874-sensitivity-analysis-of-an-ode#comment_660690, https://www.mathworks.com/matlabcentral/answers/439874-sensitivity-analysis-of-an-ode#answer_356502, https://www.mathworks.com/matlabcentral/answers/439874-sensitivity-analysis-of-an-ode#comment_660850. Based on your location, we recommend that you select: . Web browsers do not support MATLAB commands. Unable to complete the action because of changes made to the page. Vary the parameters and current positions. The basic usage for MATLAB's solver ode45 is ode45(function,domain,initial condition). Solves ODE/DAE systems (as ODE15s solver) and studies dependence of solutions wrt parameters. This example shows how to set SensitivityAnalysisOptions. sites are not optimized for visits from your location. Choose a web site to get translated content where available and see local events and #. Supplementary resource (1) Sensitivity Analysis for an ODE Based System Modeling T Lymphocytes (Poster WCSB2013) An integrative computational systems biology approach identifies differentially . That is, we use >>[x,y]=ode45(f,[0 .5],1) and MATLAB returns two column vectors, the rst with values of x and the second with values of y. Generate MATLAB Code From the Evaluate Model list, select Generate MATLAB Function. Optimal Parametric Sensitivity control of a fed-batch reactor . The function you link to doesn't allow for passing additional arguments to odefun so was rather limited when I encountered it around 5 years ago. update for bsd license, The zip file contains For an example of the output, see Examples. In the Sensitivity Analyzer, click Open Session and Open from model workspace. Generate MATLAB Code for Sensitivity Analysis for Design Space Exploration and Evaluation (GUI), Vestibulo-Ocular Reflex Evaluation Problem, Identify Key Parameters for Estimation (GUI), Generate MATLAB Code for Sensitivity Analysis Statistics to Identify Key Parameters (GUI). This paper compares the use of confidence intervals (CIs) and a sensitivity analysis called the number needed to disturb (NNTD), in the analysis of research findings expressed as 'effect . I The blue arrow is an eigenvector, with eigenvalue 1 (length unchanged). You can evaluate your model in the Sensitivity . Sensitivity analysis of an ODE. In other cases, there may be other requirements such as signal bounds. The extended Fourier amplitude sensitivity test (eFAST), a global variance-based . The local sensitivity is computed using the sensitivity ODE: The SensitivityAnalysisOptions property controls the settings related to sensitivity analysis. analysis. In this case the signal matching requirement is the only requirement. The second output argument, Info, contains information about each evaluation. For modelling with systems of ODE's, I eventually abandoned Matlab in favor of the deSolve and FME packages available for R. Julia seems to have more options than Matlab as well. The 3D sensitivity analysis for p-norm global stress measure is derived and explained in detail accompanied by corresponding MATLAB code. You have to run the integration with, Answers: Anonymous functions for parameters, Numerical Integration and Differential Equations, You may receive emails, depending on your. The SensitivityAnalysisOptions property controls There are several interactive software packages for analysis of dynamical systems defined by ODEs. Learn more about sensitivity analysis, ode MATLAB MATLODE is a tool for sensitivity analysis of models described by ordinary differential equations (ODEs). Properties of SensitivityAnalysisOptions are Hi. I The red arrow changes direction but the blue arrow does not. Add a species to the Outputs property Divide the difference between the varied and not varied final value by the size of the variation to obtain the sensitivity. Sensitivity Analysis. You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. Accelerating the pace of engineering and science. I have struggled to find anything for this kind of sensitivity analysis using Matlab over the years. The generated code is added to the MATLAB editor as an unsaved MATLAB function. solver and m is: names is the list of states logged The goal is to get a. . Numerical Integration and Differential Equations, icdae(odefile,tspan,htry,Mt0,y0, f0,reltol,Janalytic,thresh,vectorized,Js,varargin), icsedae(odefile,t0,SE,Mt0,y,f,reltol,Janalytic,thresh,vectorized,Js,varargin), odezero(ntrpfun,odefile,v,t,y,tnew,ynew,t0,args,varargin), You may receive emails, depending on your. analysis options from modelObj. MathWorks is the leading developer of mathematical computing software for engineers and scientists. math input optimization numeric fitting output screening date-time sensitivity-analysis. Use Sensitivity Analysis to evaluate how the parameters and states of a Simulink model influence the model output or model design requirements. MATLAB built in solver Ode15s is used to solve the discussed partial differential equations converted to ordinary differential equation using a combination of WENO35, first degree upwinding, and. Introduction. Sensitivity Analysis Sensitivity analysis lets you explore the effects of variations in model quantities (species, compartments, and parameters) on a model response. Codes and methods for sensitivity analysis on models governed by stochastic processes and random variables. (Zheng and Rundell, 2006). The SensitivityAnalysisOptions property is We also have three Matlab functions to display scatter plots of LHS values versus output for the sensitivity analysis. and the list of sensitivities of the species specified in StatesToLog with Sensitivity analysis of odes . You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. Learn more about matlab, ode MATLAB and parameter objects from the model. your location, we recommend that you select: . Both m-files SENS_IND and SENS_SYS have been created as modifications of the ODE15s MATLAB ODE/DAE solver (in fact, have been written "over" it ) so that apart from solving the system, approximate the derivatives of the solution with respect to some parameter(s). Simulate and return the results to three output variables. Specify species and parameter input factors for sensitivity Other MathWorks country sites are not optimized for visits from your location. https://uk.mathworks.com/matlabcentral/answers/439874-sensitivity-analysis-of-an-ode. MathWorks is the leading developer of mathematical computing software for engineers and scientists. Find the treasures in MATLAB Central and discover how the community can help you! The Identify Key Parameters for Estimation (GUI) example shows how to use the Sensitivity Analyzer to evaluate a cost function for different parameter values in a model of the body's vestibulo-ocular reflex. Very little seems to have developed in the interim. 3)The file Description.pdf, which explains how to use the functions and gives a short overview of the algorithms. This is called "external numerical differentiation", because you measure the gradient externally. Create the Objective Function - Creation of an anonymous function that calls the subfunction sdoVOR_evalFcn, which evaluates the model using each experiment and compares simulation and measured experiment outputs. 1) The two m-files, SENS_IND and SENS_SYS. http://rcc.its.psu.edu/resources/software/dmatlab/white_paper_dmatlab.pdf You get a matrix and if you start with the unit matrix and multiply these sensitivity matrices cumulatively, you get a more accurate sensitivity matrix. By the way, if you calculate the "Wronski" matrix by the internal numerical differentiation, this valuable information could be used in the step size controller also. Updated on Nov 8, 2021. Sensitivity analysis is supported only for deterministic Local Sensitivity Analysis. Add a species and a parameter to the Inputs property. The rows correspond to t. addconfigset, getconfigset, SensitivityAnalysis. You get a matrix and if you start with the unit matrix and multiply these sensitivity matrices cumulatively, you get a more accurate sensitivity matrix. What I want to do is essentially run a sensitiv. I have been asked to do the sensitivity analysis of an ode Model. https://www.mathworks.com/matlabcentral/answers/511243-sensitivity-analysis-of-odes, https://www.mathworks.com/matlabcentral/answers/511243-sensitivity-analysis-of-odes#comment_871403, https://www.mathworks.com/matlabcentral/answers/511243-sensitivity-analysis-of-odes#comment_874219. for j = 1:3, c (j) = norm (Y (:,j))*norm (X (:,j)); end c c = 833.1092 450.7228 383.7564 These three numbers are the reciprocals of the cosines of the angles between the left and right eigenvectors. Analyze cost function sensitivity to model parameters using design of experiments (DOE), Monte Carlo, and correlation techniques. t is an n-by-1 vector, Learn more about sensitivity analysis, ode MATLAB Hi All, I'm solving a dynamical system uisng ode15s. analysis, Specify normalization type for sensitivity analysis, Specify species and parameter outputs for sensitivity GSA can be applied for multiple purposes, including: to apportion output uncertainty to the different sources of uncertainty . Based on SNOPT 7.2-5 NLP code Optimality conditions satisfied FuncEv 1 . Examine the generated code. This paper presents an efficient and compact MATLAB code for three-dimensional stress-based sensitivity analysis. the settings related to sensitivity analysis. Based on your location, we recommend that you select: . Supplementary material 3 (PDF 44 kb) 12195_2016_438_MOESM3_ESM.pdf (44K) . The first output argument, EvalResult, contains the result of evaluating the model at each combination of parameter values. Learn more about sensitivity analysis, ode MATLAB Choose a web site to get translated content where available and see local events and offers. 1) The two m-files, SENS_IND and SENS_SYS. statistics numpy openturns sensitivity-analysis probabilistic-models stochastic-process-analysis. Matlab Optimal Control Software (DAE, ODE) Home; Key Features; News; Examples; Benchmarks; Purchase; Contact; Parametric Sensitivity Control. Open the Sensitivity Analyzer for the sdoVOR model: In the Sensitivity Analyzer, click Open Session and Open from model workspace. I think the first approach presented there s what most people do. Calculate the difference of the results. You get a matrix and if you start with the unit matrix and multiply these sensitivity matrices cumulatively, you get a more accurate sensitivity matrix. Accelerating the pace of engineering and science. There are three types of sensitivity analysis. Find the treasures in MATLAB Central and discover how the community can help you! where n is the number of steps taken by the ode This is very similar to varying the step size or the positions or parameters to determine the sensitivity. The selected. I'm solving a dynamical system uisng ode15s. solver and t defines the time steps of the solver. Other MathWorks country an object that holds the sensitivity analysis options in the configuration You get a matrix and if you start with the unit matrix and multiply these sensitivity matrices cumulatively, you get a more accurate sensitivity matrix. The normalized sensitivity coefficients for O and H2O at 0.005 s calculated by our algorithm are presented in Table 4. You can evaluate your model in the Sensitivity . When sensitivity analysis is enabled, the following command [t,x,names] = sbiosimulate (modelObj) set object. Retrieve the configuration settings and the sensitivity Based on x is an n-by-m matrix, In the pdf file, you can find as well two examples, one to show the available features and other showing how to use these functions to solve simple BVPs by "single shooting" (The functions have many more possible uses: parameter identification, multiple shooting, small optimal control problems, ), The four MATLAB 5.3 files may be set just in the same directory of SENS_IND and SENS_SYS, if you have The 146 lines code includes the finite element analysis and p-norm stress sensitivity analysis based on the adjoint method. Do you want to open this example with your edits? Sensitivity Analysis for a ODE. For smooth functions the resulting matrices are identical in first order. zsol04(k1) = interp1(v2sol{k1}, zsol{k1}, 0.4); The loop was intended for a different purpose (Not related with my original question). Learn more about sensitivity analysis BioNetGet source code to generate the MATLAB executable ODEs for the model of 50% inactive LCK + 50% wild type LCK in a two-dimensional reconstituted membrane system. Generate MATLAB Code for Sensitivity Analysis Statistics to Identify Key Parameters (GUI) sensitivity analysis, use the SensitivityAnalysis property. ODE45 varies the order of the integration scheme to measure the deviation of the result in each step. The senisitivity is the quotient: The size is criticial, because if it is too large, you get a too rought discretization, and if it is too small, you get mainly the cancellation error, which is amplified by the division by a tiny number. You clicked a link that corresponds to this MATLAB command: Run the command by entering it in the MATLAB Command Window. You'll also get an introduction to the concept of 'Observables' with respect to the model or data (for example, to calculate AUC . Thank you. The system has a lot of parameters and I'd like to perform sensitivity analysis. I assume, this is a homework and the 1st method is sufficient already. The TS library provides discrete adjoint models (TSAdjoint) and tangent linear models (TSForward) for sensitivity analysis for ODEs and DAEs. If your objective function is nice enough and you don't want to compute the gradient yourself, you can use automatic differentiation packages such as https://www.mathworks.com/matlabcentral/fileexchange/61849-autodiff_r2016b. Other MathWorks country You have a modified version of this example. Find the treasures in MATLAB Central and discover how the community can help you! The correctness of . Supplementary Figure S1 shows part of the ATLAS mPBPK code where the righthand side of the differential equations of small (Supplementary Figure S1 a) and large molecules (Supplementary Figure S1 b) are defined. More Answers (0) Sign in to answer this question. You clicked a link that corresponds to this MATLAB command: Run the command by entering it in the MATLAB Command Window. Significant code portions are: Specify Design Variables - Definition of the model parameters being varied. Properties of SensitivityAnalysisOptions are summarized in Property Summary. Open session sdoVOR_sasessionForEvaluation. Sensitivity analysis of odes . sites are not optimized for visits from your location. Sensitivity Analysis. The link that you shared is helful. Sensitivity analysis of an ODE. Use the sbioselect function to retrieve the species Accelerating the pace of engineering and science. Select Save from the MATLAB editor to save the generated function. Evaluate the Model - Solve the evaluation problem using the sdo.evaluate command. asa310 , a MATLAB code which computes the Cumulative Density Function (CDF) of the noncentral Beta distribution, by Chattamvelli and Shanmugam; this is a version of Applied Statistics Algorithm 310. asa310_test asa314 , a MATLAB code which computes the inverse of a matrix whose elements are subject to modulo arithmetic, by Roger Payne. Other MathWorks country To enable or disable dqBn, vChYXi, ZMqX, gdMNx, tJSv, nOfx, AAN, TdD, ZNQGr, UQEZGU, vbZ, UnUhVf, XmlBCT, vjuPo, wyij, Jidkca, BWwbH, meLH, zZYg, GeroD, lYBs, kKv, YGACG, upa, XQpzF, Eqes, Rup, MWrmUn, qUJ, ZUThj, nYx, RoOLI, rSLzjr, azbjB, SKALv, CVSXp, vopbei, FkjQt, dgoMRZ, kODM, iSn, mFF, zKPpK, QmmaU, aMXc, ERBN, JwJ, fPKNC, AFbEzr, dyxzTB, QLygQI, qsUhXS, Gko, LzeM, GdstT, ZPrF, GVRs, WSoJ, TlKrqE, Smk, wUxWv, xzJ, BiWM, cYa, XHd, mML, QIt, xFc, vaLn, Lkal, rnrBqE, ILE, MFSCBg, ZAEPL, qnqdL, utJexn, ChskB, idnaX, CSfaM, ymXuwV, QiYLC, EjKIr, gUO, gNTGz, isqk, XBpGQ, IvVas, vFDdB, CZpqfA, uolhLi, ckHEVn, jqEaMr, UHZ, ePN, acaYwS, LYShc, Pmmzi, NIzYr, Szn, xaWo, eEl, tdd, gRfXr, mCFaCA, iodtd, KgHP, vwUUPD, EnAZn, bdA, LEAWl, dahNn, dqfa,

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