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<!-- generated with COPASI 4.12 (Build 79) (http://www.copasi.org) at 2014-04-15 07:27:53 UTC -->
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<ListOfFunctions>
<Function key="Function_13" name="Mass action (irreversible)" type="MassAction" reversible="false">
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<b>Mass action rate law for first order irreversible reactions</b>
<p>
Reaction scheme where the products are created from the reactants and the change of a product quantity is proportional to the product of reactant activities. The reaction scheme does not include any reverse process that creates the reactants from the products. The change of a product quantity is proportional to the quantity of one reactant.
</p>
</body>
</Comment>
<Expression>
k1*PRODUCT<substrate_i>
</Expression>
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<ParameterDescription key="FunctionParameter_81" name="k1" order="0" role="constant"/>
<ParameterDescription key="FunctionParameter_79" name="substrate" order="1" role="substrate"/>
</ListOfParameterDescriptions>
</Function>
</ListOfFunctions>
<Model key="Model_10" name="The Brusselator" simulationType="time" timeUnit="s" volumeUnit="ml" areaUnit="m²" lengthUnit="m" quantityUnit="mmol" type="deterministic" avogadroConstant="6.0221415e+023">
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<dcterms:W3CDTF>2014-04-15T09:23:42Z</dcterms:W3CDTF>
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<p>The famous Brusselator model in which a chemical species X catalyses its own formation. In a certain region of parameter space the Brusselator can function in a limit cycle regime around an unstable steady state. Run this simulation and then check the report file to see how Gepasi can find an unstable steady state, and calculate the eigenvalues of the Jacobian matrix. </p>
</body></html>
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<ListOfCompartments>
<Compartment key="Compartment_6" name="compartment" simulationType="fixed" dimensionality="3">
</Compartment>
</ListOfCompartments>
<ListOfMetabolites>
<Metabolite key="Metabolite_21" name="X" simulationType="reactions" compartment="Compartment_6">
</Metabolite>
<Metabolite key="Metabolite_14" name="Y" simulationType="reactions" compartment="Compartment_6">
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<dcterms:W3CDTF>2014-04-15T09:23:51Z</dcterms:W3CDTF>
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<Metabolite key="Metabolite_44" name="A" simulationType="fixed" compartment="Compartment_6">
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<dcterms:W3CDTF>2014-04-15T09:23:50Z</dcterms:W3CDTF>
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</Metabolite>
<Metabolite key="Metabolite_46" name="B" simulationType="fixed" compartment="Compartment_6">
</Metabolite>
<Metabolite key="Metabolite_48" name="D" simulationType="fixed" compartment="Compartment_6">
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</Metabolite>
<Metabolite key="Metabolite_50" name="E" simulationType="fixed" compartment="Compartment_6">
</Metabolite>
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<ListOfReactions>
<Reaction key="Reaction_3" name="R1" reversible="false" fast="false">
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<ListOfSubstrates>
<Substrate metabolite="Metabolite_44" stoichiometry="1"/>
</ListOfSubstrates>
<ListOfProducts>
<Product metabolite="Metabolite_21" stoichiometry="1"/>
</ListOfProducts>
<ListOfConstants>
<Constant key="Parameter_4227" name="k1" value="1"/>
</ListOfConstants>
<KineticLaw function="Function_13">
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<CallParameter functionParameter="FunctionParameter_81">
<SourceParameter reference="Parameter_4227"/>
</CallParameter>
<CallParameter functionParameter="FunctionParameter_79">
<SourceParameter reference="Metabolite_44"/>
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</KineticLaw>
</Reaction>
<Reaction key="Reaction_2" name="R2" reversible="false" fast="false">
<ListOfSubstrates>
<Substrate metabolite="Metabolite_21" stoichiometry="2"/>
<Substrate metabolite="Metabolite_14" stoichiometry="1"/>
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<ListOfProducts>
<Product metabolite="Metabolite_21" stoichiometry="3"/>
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<ListOfConstants>
<Constant key="Parameter_4226" name="k1" value="1"/>
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<KineticLaw function="Function_13">
<ListOfCallParameters>
<CallParameter functionParameter="FunctionParameter_81">
<SourceParameter reference="Parameter_4226"/>
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<CallParameter functionParameter="FunctionParameter_79">
<SourceParameter reference="Metabolite_21"/>
<SourceParameter reference="Metabolite_21"/>
<SourceParameter reference="Metabolite_14"/>
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</ListOfCallParameters>
</KineticLaw>
</Reaction>
<Reaction key="Reaction_1" name="R3" reversible="false" fast="false">
<ListOfSubstrates>
<Substrate metabolite="Metabolite_21" stoichiometry="1"/>
<Substrate metabolite="Metabolite_46" stoichiometry="1"/>
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<ListOfProducts>
<Product metabolite="Metabolite_14" stoichiometry="1"/>
<Product metabolite="Metabolite_48" stoichiometry="1"/>
</ListOfProducts>
<ListOfConstants>
<Constant key="Parameter_4225" name="k1" value="1"/>
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<KineticLaw function="Function_13">
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<CallParameter functionParameter="FunctionParameter_81">
<SourceParameter reference="Parameter_4225"/>
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<CallParameter functionParameter="FunctionParameter_79">
<SourceParameter reference="Metabolite_21"/>
<SourceParameter reference="Metabolite_46"/>
</CallParameter>
</ListOfCallParameters>
</KineticLaw>
</Reaction>
<Reaction key="Reaction_0" name="R4" reversible="false" fast="false">
<ListOfSubstrates>
<Substrate metabolite="Metabolite_21" stoichiometry="1"/>
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<ListOfProducts>
<Product metabolite="Metabolite_50" stoichiometry="1"/>
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<ListOfConstants>
<Constant key="Parameter_4224" name="k1" value="1"/>
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<KineticLaw function="Function_13">
<ListOfCallParameters>
<CallParameter functionParameter="FunctionParameter_81">
<SourceParameter reference="Parameter_4224"/>
</CallParameter>
<CallParameter functionParameter="FunctionParameter_79">
<SourceParameter reference="Metabolite_21"/>
</CallParameter>
</ListOfCallParameters>
</KineticLaw>
</Reaction>
</ListOfReactions>
<ListOfModelParameterSets activeSet="ModelParameterSet_0">
<ModelParameterSet key="ModelParameterSet_0" name="Initial State">
<ModelParameterGroup cn="String=Initial Time" type="Group">
<ModelParameter cn="CN=Root,Model=The Brusselator" value="0" type="Model" simulationType="time"/>
</ModelParameterGroup>
<ModelParameterGroup cn="String=Initial Compartment Sizes" type="Group">
<ModelParameter cn="CN=Root,Model=The Brusselator,Vector=Compartments[compartment]" value="1" type="Compartment" simulationType="fixed"/>
</ModelParameterGroup>
<ModelParameterGroup cn="String=Initial Species Values" type="Group">
<ModelParameter cn="CN=Root,Model=The Brusselator,Vector=Compartments[compartment],Vector=Metabolites[X]" value="1.80664e+021" type="Species" simulationType="reactions"/>
<ModelParameter cn="CN=Root,Model=The Brusselator,Vector=Compartments[compartment],Vector=Metabolites[Y]" value="1.80664e+021" type="Species" simulationType="reactions"/>
<ModelParameter cn="CN=Root,Model=The Brusselator,Vector=Compartments[compartment],Vector=Metabolites[A]" value="3.01107e+020" type="Species" simulationType="fixed"/>
<ModelParameter cn="CN=Root,Model=The Brusselator,Vector=Compartments[compartment],Vector=Metabolites[B]" value="1.80664e+021" type="Species" simulationType="fixed"/>
<ModelParameter cn="CN=Root,Model=The Brusselator,Vector=Compartments[compartment],Vector=Metabolites[D]" value="0" type="Species" simulationType="fixed"/>
<ModelParameter cn="CN=Root,Model=The Brusselator,Vector=Compartments[compartment],Vector=Metabolites[E]" value="0" type="Species" simulationType="fixed"/>
</ModelParameterGroup>
<ModelParameterGroup cn="String=Initial Global Quantities" type="Group">
</ModelParameterGroup>
<ModelParameterGroup cn="String=Kinetic Parameters" type="Group">
<ModelParameterGroup cn="CN=Root,Model=The Brusselator,Vector=Reactions[R1]" type="Reaction">
<ModelParameter cn="CN=Root,Model=The Brusselator,Vector=Reactions[R1],ParameterGroup=Parameters,Parameter=k1" value="1" type="ReactionParameter" simulationType="fixed"/>
</ModelParameterGroup>
<ModelParameterGroup cn="CN=Root,Model=The Brusselator,Vector=Reactions[R2]" type="Reaction">
<ModelParameter cn="CN=Root,Model=The Brusselator,Vector=Reactions[R2],ParameterGroup=Parameters,Parameter=k1" value="1" type="ReactionParameter" simulationType="fixed"/>
</ModelParameterGroup>
<ModelParameterGroup cn="CN=Root,Model=The Brusselator,Vector=Reactions[R3]" type="Reaction">
<ModelParameter cn="CN=Root,Model=The Brusselator,Vector=Reactions[R3],ParameterGroup=Parameters,Parameter=k1" value="1" type="ReactionParameter" simulationType="fixed"/>
</ModelParameterGroup>
<ModelParameterGroup cn="CN=Root,Model=The Brusselator,Vector=Reactions[R4]" type="Reaction">
<ModelParameter cn="CN=Root,Model=The Brusselator,Vector=Reactions[R4],ParameterGroup=Parameters,Parameter=k1" value="1" type="ReactionParameter" simulationType="fixed"/>
</ModelParameterGroup>
</ModelParameterGroup>
</ModelParameterSet>
</ListOfModelParameterSets>
<StateTemplate>
<StateTemplateVariable objectReference="Model_10"/>
<StateTemplateVariable objectReference="Metabolite_21"/>
<StateTemplateVariable objectReference="Metabolite_14"/>
<StateTemplateVariable objectReference="Metabolite_44"/>
<StateTemplateVariable objectReference="Metabolite_46"/>
<StateTemplateVariable objectReference="Metabolite_48"/>
<StateTemplateVariable objectReference="Metabolite_50"/>
<StateTemplateVariable objectReference="Compartment_6"/>
</StateTemplate>
<InitialState type="initialState">
0 1.80664e+021 1.80664e+021 3.01107e+020 1.80664e+021 0 0 1
</InitialState>
</Model>
<ListOfTasks>
<Task key="Task_12" name="Steady-State" type="steadyState" scheduled="false" updateModel="false">
<Report reference="Report_0" target="" append="1" confirmOverwrite="0"/>
<Problem>
<Parameter name="JacobianRequested" type="bool" value="1"/>
<Parameter name="StabilityAnalysisRequested" type="bool" value="1"/>
</Problem>
<Method name="Enhanced Newton" type="EnhancedNewton">
<Parameter name="Resolution" type="unsignedFloat" value="1e-009"/>
<Parameter name="Derivation Factor" type="unsignedFloat" value="0.001"/>
<Parameter name="Use Newton" type="bool" value="1"/>
<Parameter name="Use Integration" type="bool" value="0"/>
<Parameter name="Use Back Integration" type="bool" value="0"/>
<Parameter name="Accept Negative Concentrations" type="bool" value="0"/>
<Parameter name="Iteration Limit" type="unsignedInteger" value="50"/>
<Parameter name="Maximum duration for forward integration" type="unsignedFloat" value="1000000000"/>
<Parameter name="Maximum duration for backward integration" type="unsignedFloat" value="1000000"/>
</Method>
</Task>
<Task key="Task_1" name="Time-Course" type="timeCourse" scheduled="false" updateModel="false">
<Problem>
<Parameter name="StepNumber" type="unsignedInteger" value="200"/>
<Parameter name="StepSize" type="float" value="0.5"/>
<Parameter name="Duration" type="float" value="100"/>
<Parameter name="TimeSeriesRequested" type="bool" value="1"/>
<Parameter name="OutputStartTime" type="float" value="2"/>
<Parameter name="Output Event" type="bool" value="0"/>
<Parameter name="Continue on Simultaneous Events" type="bool" value="0"/>
</Problem>
<Method name="Deterministic (LSODA)" type="Deterministic(LSODA)">
<Parameter name="Integrate Reduced Model" type="bool" value="1"/>
<Parameter name="Relative Tolerance" type="unsignedFloat" value="1e-006"/>
<Parameter name="Absolute Tolerance" type="unsignedFloat" value="1e-012"/>
<Parameter name="Max Internal Steps" type="unsignedInteger" value="10000"/>
</Method>
</Task>
<Task key="Task_2" name="Metabolic Control Analysis" type="metabolicControlAnalysis" scheduled="false" updateModel="false">
<Report reference="Report_5" target="" append="1" confirmOverwrite="0"/>
<Problem>
<Parameter name="Steady-State" type="key" value="Task_12"/>
</Problem>
<Method name="MCA Method (Reder)" type="MCAMethod(Reder)">
<Parameter name="Modulation Factor" type="unsignedFloat" value="1e-009"/>
</Method>
</Task>
<Task key="Task_3" name="Scan" type="scan" scheduled="false" updateModel="false">
<Problem>
<Parameter name="Subtask" type="unsignedInteger" value="1"/>
<ParameterGroup name="ScanItems">
</ParameterGroup>
<Parameter name="Output in subtask" type="bool" value="1"/>
<Parameter name="Adjust initial conditions" type="bool" value="0"/>
</Problem>
<Method name="Scan Framework" type="ScanFramework">
</Method>
</Task>
<Task key="Task_4" name="Optimization" type="optimization" scheduled="false" updateModel="false">
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<Problem>
<Parameter name="Subtask" type="cn" value="Vector=TaskList[Time-Course]"/>
<ParameterText name="ObjectiveExpression" type="expression">
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<Parameter name="Maximize" type="bool" value="0"/>
<Parameter name="Randomize Start Values" type="bool" value="0"/>
<Parameter name="Calculate Statistics" type="bool" value="1"/>
<ParameterGroup name="OptimizationItemList">
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<ParameterGroup name="OptimizationConstraintList">
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<Parameter name="ObjectiveFunction" type="key" value=""/>
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<Method name="Random Search" type="RandomSearch">
<Parameter name="Number of Iterations" type="unsignedInteger" value="100000"/>
<Parameter name="Random Number Generator" type="unsignedInteger" value="1"/>
<Parameter name="Seed" type="unsignedInteger" value="0"/>
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<Task key="Task_5" name="Parameter Estimation" type="parameterFitting" scheduled="false" updateModel="false">
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<Parameter name="Maximize" type="bool" value="0"/>
<Parameter name="Randomize Start Values" type="bool" value="0"/>
<Parameter name="Calculate Statistics" type="bool" value="1"/>
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<ParameterGroup name="OptimizationConstraintList">
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<Parameter name="Steady-State" type="cn" value="CN=Root,Vector=TaskList[Steady-State]"/>
<Parameter name="Time-Course" type="cn" value="CN=Root,Vector=TaskList[Time-Course]"/>
<ParameterGroup name="Experiment Set">
</ParameterGroup>
<ParameterGroup name="Validation Set">
<Parameter name="Threshold" type="unsignedInteger" value="5"/>
<Parameter name="Weight" type="unsignedFloat" value="1"/>
</ParameterGroup>
</Problem>
<Method name="Evolutionary Program" type="EvolutionaryProgram">
<Parameter name="Number of Generations" type="unsignedInteger" value="200"/>
<Parameter name="Population Size" type="unsignedInteger" value="20"/>
<Parameter name="Random Number Generator" type="unsignedInteger" value="1"/>
<Parameter name="Seed" type="unsignedInteger" value="0"/>
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<Problem>
<Parameter name="ExponentNumber" type="unsignedInteger" value="3"/>
<Parameter name="DivergenceRequested" type="bool" value="1"/>
<Parameter name="TransientTime" type="float" value="0"/>
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<Method name="Wolf Method" type="WolfMethod">
<Parameter name="Orthonormalization Interval" type="unsignedFloat" value="1"/>
<Parameter name="Overall time" type="unsignedFloat" value="1000"/>
<Parameter name="Relative Tolerance" type="unsignedFloat" value="1e-006"/>
<Parameter name="Absolute Tolerance" type="unsignedFloat" value="1e-012"/>
<Parameter name="Max Internal Steps" type="unsignedInteger" value="10000"/>
<Parameter name="Orthonormalize Intervall" type="unsignedFloat" value="1"/>
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<Problem>
</Problem>
<Method name="EFM Algorithm" type="EFMAlgorithm">
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<Task key="Task_8" name="Time Scale Separation Analysis" type="timeScaleSeparationAnalysis" scheduled="false" updateModel="false">
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<Problem>
<Parameter name="StepNumber" type="unsignedInteger" value="100"/>
<Parameter name="StepSize" type="float" value="0.01"/>
<Parameter name="Duration" type="float" value="1"/>
<Parameter name="TimeSeriesRequested" type="bool" value="1"/>
<Parameter name="OutputStartTime" type="float" value="0"/>
</Problem>
<Method name="ILDM (LSODA,Deuflhard)" type="TimeScaleSeparation(ILDM,Deuflhard)">
<Parameter name="Deuflhard Tolerance" type="unsignedFloat" value="1e-006"/>
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<Task key="Task_9" name="Sensitivities" type="sensitivities" scheduled="false" updateModel="false">
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<Parameter name="SubtaskType" type="unsignedInteger" value="1"/>
<ParameterGroup name="TargetFunctions">
<Parameter name="SingleObject" type="cn" value=""/>
<Parameter name="ObjectListType" type="unsignedInteger" value="7"/>
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<ParameterGroup name="ListOfVariables">
<ParameterGroup name="Variables">
<Parameter name="SingleObject" type="cn" value=""/>
<Parameter name="ObjectListType" type="unsignedInteger" value="41"/>
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<Method name="Sensitivities Method" type="SensitivitiesMethod">
<Parameter name="Delta factor" type="unsignedFloat" value="0.001"/>
<Parameter name="Delta minimum" type="unsignedFloat" value="1e-012"/>
</Method>
</Task>
<Task key="Task_10" name="Moieties" type="moieties" scheduled="false" updateModel="false">
<Problem>
</Problem>
<Method name="Householder Reduction" type="Householder">
</Method>
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<Task key="Task_11" name="Cross Section" type="crosssection" scheduled="false" updateModel="false">
<Problem>
<Parameter name="StepNumber" type="unsignedInteger" value="100"/>
<Parameter name="StepSize" type="float" value="0.01"/>
<Parameter name="Duration" type="float" value="1"/>
<Parameter name="TimeSeriesRequested" type="bool" value="1"/>
<Parameter name="OutputStartTime" type="float" value="0"/>
<Parameter name="Output Event" type="bool" value="0"/>
<Parameter name="Continue on Simultaneous Events" type="bool" value="0"/>
<Parameter name="LimitCrossings" type="bool" value="0"/>
<Parameter name="NumCrossingsLimit" type="unsignedInteger" value="0"/>
<Parameter name="LimitOutTime" type="bool" value="0"/>
<Parameter name="LimitOutCrossings" type="bool" value="0"/>
<Parameter name="PositiveDirection" type="bool" value="1"/>
<Parameter name="NumOutCrossingsLimit" type="unsignedInteger" value="0"/>
<Parameter name="LimitUntilConvergence" type="bool" value="0"/>
<Parameter name="ConvergenceTolerance" type="float" value="1e-006"/>
<Parameter name="Threshold" type="float" value="0"/>
<Parameter name="DelayOutputUntilConvergence" type="bool" value="0"/>
<Parameter name="OutputConvergenceTolerance" type="float" value="1e-006"/>
<ParameterText name="TriggerExpression" type="expression">
</ParameterText>
<Parameter name="SingleVariable" type="cn" value=""/>
</Problem>
<Method name="Deterministic (LSODA)" type="Deterministic(LSODA)">
<Parameter name="Integrate Reduced Model" type="bool" value="0"/>
<Parameter name="Relative Tolerance" type="unsignedFloat" value="1e-006"/>
<Parameter name="Absolute Tolerance" type="unsignedFloat" value="1e-012"/>
<Parameter name="Max Internal Steps" type="unsignedInteger" value="10000"/>
</Method>
</Task>
<Task key="Task_13" name="Linear Noise Approximation" type="linearNoiseApproximation" scheduled="false" updateModel="false">
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<Problem>
<Parameter name="Steady-State" type="key" value="Task_12"/>
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<Method name="Linear Noise Approximation" type="LinearNoiseApproximation">
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</Task>
</ListOfTasks>
<ListOfReports>
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<Comment>
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Automatically generated report.
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Automatically generated report.
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Automatically generated report.
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