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    Potential Scenario
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    2010-Brian_Winkel-Parameter estimates in differential equation models for chemical kinetics
    We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data.
    kineticschemical kineticszeroth order reactionfirst order reactionsecond order reaction
    Potential Scenario
    202

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    40

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    2012-Campbell-EtAl-Parameter estimation in differential equation models with constrained states
    We introduce a method to estimate parameters and states from a differential equation model while enforcing interpretability constraints such as monotone or non‐negative states.
    chemical engineeringsmoothing-based relaxation method
    Article or Presentation
    182

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    45

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    2011-Brian_Winkel-Parameter_Estimates_in_Differential_Equation_Models_for_Population_Growth
    We estimate the parameters present in several differential equation models of population growth, specifically single species exponential and logistic growth, and multiple species competition and predation models.
    population modelparameter estimationpopulationparameter
    Modeling Scenario
    288

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    195

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    3-130-MatterOfSomeGravity-ModelingScenario
    This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation.
    gravityinverse problemacceleration
    Article or Presentation
    188

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    69

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    2011-Brian_Winkel-Parameter_Estimates_in_Differential_Equation_Models_for_Chemical_Kinetics
    We estimate the parameters present in several differential equation models of chemical kinetics and logistic growth.
    kineticsparameter estimationlogisticchemical kineticschemical reaction
    Modeling Scenario
    276

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    169

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    0

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    3-026-SpringInverseProblem-ModelingScenario
    We are given data on the position of a mass in an oscillating spring mass system and we seek to discover approaches to estimating an unknown parameter.
    datamassinverse problemspring\parameter estimate
    Potential Scenario
    198

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    64

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    2011-Brian_Winkel-Parameter Estimates in Differential Equation Models for Population Growth
    We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and multiple species competition models.
    logisticpopulationparameciaGausegradient search
    Potential Scenario
    165

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    57

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    0

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    2019-Hu-Treinen-One-step_method_for_modelling_longitudinal_data_with_differential_equations
    This study proposes a new approach to estimate the parameters in differential equation models used to describe non-linear trajectories of longitudinal data.
    simulationparameter estimationshoppingfittingbehaviour
    Potential Scenario
    136

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    80

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    2014-Wang-EtAl-Estimating Mixed-Effects Differential Equation Models
    When multiple replicates of measurements are available for the dynamic process, it is of great interest to estimate mixed-effects in the ODE model for the process. We propose a semiparametric method to estimate mixed-effects ODE models.
    pharmacokineticsdynamic modelssmoothingsplinemixed-effects modelsHiV combination therapy
    Modeling Scenario
    221

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    166

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    4-035-ParEstSteadyState-ModelingScenario
    Students estimate parameters in a second order, linear, ordinary differential equations through analysis of the steady state solution. By applying a driver we can collect data in terms of the parameters and estimate these parameters
    driversteady statesum of square errors
    Potential Scenario
    149

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    41

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    2007-Graham-Lerch-Parameter Recovery for a Differential Equation Model
    This article presents a project for a differential equations class using an inverse problem based on the second order differential equation that models and electrical circuit.
    laboratorydata collectionRLC circuitinvers problemelectrical circuit
    Modeling Scenario
    266

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    385

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    0

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    1-094-SteepingTea-ModelingScenario
    We provide photographs of steeping process for a tea steeped in hot water. Students build a differential equation model for the steeping process and do parameter estimation using the color of our tea as a way to measure relative concentration.
    concentrationSurface AreacolorNewton's Law of Coolingteasugar
    Potential Scenario
    182

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    49

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    2012-Transtrum-Qiu-Optimal experiment selection for parameter estimation in biological differential equation models
    We explore the question to what extent parameters can be efficiently estimated by appropriate experimental selection.
    experimental designsystems biologyAssociation & Data Fittingreaction ratesdecay rates
    Potential Scenario
    132

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    46

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    2007-Ramsay-Hooker-Campbell-Cao-Parameter estimation for differential equations-a generalized smoothing approach
    We propose a new method for estimating parameters in models that are defined by a system of non-linear differential equations.
    estimating equationfunctional data analysisGauss–Newton methodparameter cascadeprofiled estimationdynamic system
    Potential Scenario
    222

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    52

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    1999-Khorasheh-Ahmadi-Gerayeli-Application of Direct Search Optimization for Pharmacokinetic Parameter Estimation
    For simple pharmacokinetic compartmental models, analytical solution to the governing differential equations provide a mean to evaluate the associated rate constants. Such methods, however, can not be used used for more complex multi-compartment...
    sum of square errorsleast squarespharmacokineticslineteicscompartmental modelsdirect search
    Potential Scenario
    360

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    62

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    0

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    2018-Hu-Huang-Dynamic Regulation Responding to an External Stimulus
    This study examines the dynamic regulation process responding to an external stimulus. This study introduces the driven damped oscillator model which has an additional parameter to identify different patterns of the steady state.
    dynamical systemsregulationsteady statesales modelexternal stimulus
    Potential Scenario
    147

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    55

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    1975-Rodda-Sampson-Smith-The One-Compartment Open Model Parameter Estimation
    A new estimation procedure is proposed for estimating the parameters of the simplest pharmacokinetic model, the one-compartment open model.
    compartment modelpharmacokineticsnonlinear estimationone compartment model
    Article or Presentation
    130

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    54

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    2011-Carl_Leinbach-Beyond_Newton_law_of_cooling_estimation_of_time_since_death
    The estimate of the time since death. Thus, the time of death is strictly that, an estimate. However, the time of death can be an important piece of information in some coroner’s cases, especially those that involve criminal or insurance...
    Newton's Law of Coolingtime of deathdouble exponentialcoroner
    Article or Presentation
    127

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    64

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    1992-Emelie_Kenney-Differential_equations_and_the_AIDS_epidemic
    This paper describes a lecture for Calculus II students in which the Acquired Immune Deficiency Syndrome was used to motivate study of first-order linear differential equations and the derivative as a rate of change.
    datafirst orderparameterAIDS
    Potential Scenario
    156

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    48

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    2009-Reid-King-Pendulum Motion and Differential Equations
    This article presents a relatively simple, real-world example that instructors can use in the classroom to let students explore the effect of simplifying assumptions on a model’s ability to reflect real-world behavior.
    pendulumphysical pendulum