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    Potential Scenario
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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
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    2008-Huangi-Lu-Modeling long-term longitudinal HIV dynamics with applications to an AIDS clinical study 
    To better understand the factors responsible for the virological failure, this paper develops the mechanism-based nonlinear differential equation models for characterizing long-term viral dynamics with ARV therapy.
    longitudinal dataAIDSantiretroviral drug therapyBayesian nonlinear mixed-effectstime-varying drug efficacyHIV dynamics
    Potential Scenario
    165

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    2014-Do-Lee-A Differential Equation Model for the Dynamics of Youth Gambling
    We examine the dynamics of gambling among young people aged 16–24 years, how prevalence rates of at-risk gambling and problem gambling change as adolescents enter young adulthood, and prevention and control strategies.
    reproductive numberGamblingepidemicsensitivity indexyouth gambling
    Potential Scenario
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    2013-Deboeck-Bergeman-The reservoir model-DE model of psychological regulation
    The following article describes a differential equation model based on the concept of a reservoir for psychological regulation.
    adaptive copingReservoirsNotre Dame Longitudinal Study on Agingoutputinput distributionstressorscoping resources
    Article or Presentation
    168

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    86

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    2015-European_Bioinformatics_Institute-Bio-Models-Database
    Bio Models Database is a repository of computational models of biological processes. Models described from literature are manually curated and enriched with cross-references. All models are provided in the Public Domain.
    biologydatabasebioinformaticsModelscomputational models
    Potential Scenario
    153

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    2017-David_Morin-Oscillations
    So needless to say, an understanding of oscillations is required for an understanding of waves.
    dampingfrequency responseresonanceoscillationbeatsunderdampingharmonic oscillatorsover dampingcritical damping
    Potential Scenario
    312

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    53

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    1999-Lomen-Lovelock-Data Sets from text Differential Equations Graphics-Models-Data
    Data selected by field is presented, e.g., chemistry, electricity, growth, motion, population, miscellaneous.
    dataEstimate
    Potential Scenario
    155

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    2015-Heiko_Enderling-Integrating experimental data to calibrate quantitative cancer models
    For quantitative cancer models to be meaningful and interpretable the number of unknown parameters must be kept minimal. We focus on a tumor hierarchy of cancer stem and progenitor non-stem cancer cells.
    cancertumorfittingagent-based
    Potential Scenario
    170

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    1999-Richard_Single-Different quotients-derivatives-and data through modeling with slime
    In this article, I present an experiment that can be conducted in a calculus class to investigate the difference quotient and the derivative, using mathematical modeling with student-collected data.
    data analysisslimedifference quotientspread of slime
    Potential Scenario
    190

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    1988-EY_Rodin-N_Taber-Yeast Growth Modelling in a Laboratory
    Modeling simple growth with some missing data and doing linear regression for parameter estimation in closed form solution of differential equation model and data.
    regressionyeastgrowth
    Potential Scenario
    186

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    44

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    2013-Alicia_Caldwell-Students Rise to the Challenge of Modeling Yeast Growth Despite Sour Hiccups from Imperfect Data
    This paper describes a lab in which students in an Applied Mathematics in Biology course observe the growth of Saccharomyces cerevisiae, a yeast strain, in differing sugar concentrations for use in learning modeling.
    Saccharomyces cerevisiaelogisticyeastdeathgrowthsugaralcohol
    Potential Scenario
    122

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    54

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    2001-Knisley-Kerley-Using data to motivate the models used in introductory differential equations
    In this paper, the data itself is used to motivate mathematical models in introductory mathematics courses. In doing so, various regression and optimization techniques are illustrated.
    regressionlogisticTorricelli's Lawgrowthperiodic process
    Potential Scenario
    154

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    59

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    2013-Greer-EtAl-Collaborative Understanding of Cyanobacteria in Lake Ecosystems
    We describe here a collaboration in which the mathematicians help collect data, the ecologists synthesize more data from model output than they can produce empirically, and the collaboration produces both mathematical approaches and field work.
    collaborationlakeecosystemcyanobacteriafield workcolonyGloeo
    Potential Scenario
    173

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    43

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    2007-Hui_Luo-Population Modeling by Differential Equations
    A general model for the population of Tibetan antelope is constructed. The present model shows that the given data is reasonably logistic.
    population dynamicsextinctionlogisticTibetan antelope
    Potential Scenario
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    1994-S_S_Everingham-C_Peter_Rydell-Modeling the Demand for Cocaine
    This is a report prepared for the Office of National Drug Control Policy of the United States Army by the Rand Corporation. The report contains lots of data and builds a two compartment difference equation model.
    drugstwo compartmentcocainedemand
    Article or Presentation
    187

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    57

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    2011-Brian_Winkel-Sourcing_for_parameter_estimation_and_study_of_logistic_differential_equation
    We present two simulation activities for students to generate real data and several data sources for the purpose of estimating parameters in the logistic differential equation model.
    dataparameter estimationparameterlogistic equationsource
    Potential Scenario
    166

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    1999-Kowalczyk-Hausknecht-Using DEs To Model Real World Data
    With the increasing availability of easy to use interactive differential equation software, we convinced ourselves to completely redesign the way we teach differential equations.
    circuitTorricelli's LawHooke's LawRC circuitharmonic oscillatorglucoseglucose tolerance test
    Potential Scenario
    160

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    48

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    1969-Carl_Metzler-A mathematical model for the pharmacokinetics of LSD effect
    Contains data on performance scores vs. plasma levels of LSD in human tissues.
    LSDtestingpharmacokineticsperformanceplasma level
    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
    240

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    2017-Floyd_Ballard-Dice Activities for DE Models
    This document includes descriptions of four activities that are appropriate for a calculus or differential equations class, all using dice to motivate a differential equation model for a real-world scenario.
    simulationcurve fittingcdicecollect dataclass activitiesanalyze dataclass activity