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6-026-S-FakingGause
30 Oct 2020 | | Contributor(s):: Brian Winkel
We use a fake or toy data set to permit discovery of the parameters in a two population protozoan model used to study paramecium and yeast competiton in the 1930's studies of G.~F.~Gause in the Soviet Union.
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1-124-S-WorldPopulation
30 May 2020 | | Contributor(s):: Lenka Pribylova, Jan Sevcik, Pavel Morcinek, Brian Winkel
We build models of world population using data to estimate growth rate.CZECH LANGUAGE VERSION We have placed in Supporting Docs a Czech version of this Student Modeling Scenario. Name will be x-y-S-Title-StudentVersion-Czech.
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3-026-S-SpringInverseProblem
29 May 2020 | | Contributor(s):: Brian Winkel
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.
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5-010-S-DNADegradation
21 Apr 2020 | | Contributor(s):: Brian Winkel
We ask students to use the system of first order linear differential equations given in a source paper and estimates of the data from laboratory procedures from a plot to estimate the parameters and complete the modeling process. Then we seek to compare the results of the final model with...
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1-126-S-MarriageMath
14 Apr 2020 | | Contributor(s):: Erdi KARA
We will explore a model which describes the process of entry into marriage by an individual. In the model, rate of change in the fraction of the cohort already married will be investigated along with two governing assumptions; social pressure experienced by unmarried individual increases as...
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2019-Hu-ModellingLongitudinalDataWithDEs
06 Apr 2020 | | Contributor(s):: Brian Winkel
2019-Hu-ModellingLongitudinalDataWithDEsHu,Yueqin and Raymond Treinen. 2019. A one-step method for modelling longitudinal datawith differential equations. British Journal of Mathematical and Statistical Psychology. 72: 38–60Abstract: Differential equation models...
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1975-RoddaEtAl-OneCompartmentOpenModel - SomeStatisticalAspectsOfParameterEstimation
06 Apr 2020 | | Contributor(s):: Brian Winkel
1975-RoddaEtAl-OneCompartmentOpenModelSomeStatisticalAspectsOfParameterEstimation The One-Compartment Open Model: Some Statistical Aspects of Parameter EstimationRodda, B. E., C. B. Sampson, D. W. Smith.1975. The One-Compartment Open Model: Some Statistical Aspects of...
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2007-HelfgottSeier-MathStatAspectsOfEnzymeKinetics
05 Apr 2020 | | Contributor(s):: Brian Winkel
2007-HelfgottSeier-MathStatAspectsOfEnzymeKineticsHelfgott, Michel and Edith Seier. 2007. Some Mathematical and Statistical Aspects of Enzyme Kinetics.The Journal of Online Mathematics and Its Applications. Volume 7, October 2007, Article ID 1611Abstract: Most...
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2012-TranstrumQiui-OptimalExperimentSelectionForParameterEstimationInBioDEs
02 Apr 2020 | | Contributor(s):: Brian Winkel
2012-TranstrumQiui-OptimalExperimentSelectionForParameterEstimationInBioDEsTranstrum, Mark K and Peng Qiu. 2012. Optimal experiment selection for parameter estimation in biological differential equation models. Bioinformatics. 13(181): 1-12.AbstractBackground:...
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2018-AdenjiEtAl-InverseProblemHolling-TannerModel
02 Apr 2020 | | Contributor(s):: Brian Winkel
2018-AdenjiEtAl-InverseProblemHolling-TannerModelAdeniji, Adejimi Adesola, Igor Fedotov, Michael Y. Shatalov. 2018. Inverse problem of theHolling-Tanner model and its solution. Biomath. 7: 1812057. 10 pages.Abstract: In this paper we undertake to consider the inverse problem of...
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2013-Rihan-DelyDEsBioScience-ParameterEstimation
01 Apr 2020 | | Contributor(s):: Brian Winkel
2013-Rihan-DelyDEsBioScience-ParameterEstimationRihan, Fathalla A. 2013. Delay Differential Equations in Biosciences: Parameter estimation and sensitivity analysis. Proceedings of the 2013 International Conference on Applied Mathematics and Computational Methods. pp....
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2017-NguyenEtAl-ParameterEstimationViralInfections
01 Apr 2020 | | Contributor(s):: Brian Winkel
2017-NguyenEtAl-ParameterEstimationViralInfectionsNguyen, Van Kinh and Esteban A. Hernandez-Vargas. 2018. Parameter estimation in mathematical models of viral infections using R. Methods Mol Biol. 1836: 531-549.Abstract: In recent years, mathematical modeling...
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2007-RamseyEtAl-ParameterEstforDE-SmoothingApproach
01 Apr 2020 | | Contributor(s):: Brian Winkel
2007-RamseyEtAl-ParameterEstforDE-SmoothingApproachJ. R. Statist. Soc. B (2007)69, Part 5, pp. 741–796Ramsay, J. O.. G. Hooker, D. Campbell and J. Cao. 2007. Parameter estimation for differential equations: a generalized smoothing approach. J. R. Statist. Soc....
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2012-CampbellEetAl-Parameter estimation in differential equation models with constrained states
26 Mar 2020 | | Contributor(s):: Brian Winkel
2012-CampbellEetAl-Parameter estimation in differential equation models with constrained statesCampbell, David A., Giles Hooker, and Kim B. McAuley. 2012. Parameter estimation in differential equation models with constrained states. Journal of Chemometrics....
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2017-SimEtAl-OptControl-CoupledTanksSystem
25 Mar 2020 | | Contributor(s):: Brian Winkel
2017-SimEtAl-OptControl-CoupledTanksSystemSim, Sy Yi, Sie Long Kek, and Kim Gaik Tay. 2017. Optimal control of a coupled tanks system with model-reality differences. AIP Conference Proceedings. 1872, 020012.Abstract: Abstract. In this paper, an efficient computational...
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2000-Erdman-StudyOfKinetics-FirstOrderODE
25 Mar 2020 | | Contributor(s):: Brian Winkel
2000-Erdman-StudyOfKinetics-FirstOrderODEErdman, Donald and Maurice M. Morelock. 2000. A Study of Kinetics: The Estimation and Simulation of Systems of First-Order Differential Equations. Notes. 8 pp. Abstract: This paper introduces new and old features of the SAS System...
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2018-AkmanEtAl-ParameterEstimationinODE-ParticlaSwarmOptimimzation
24 Mar 2020 | | Contributor(s):: Brian Winkel
2018-AkmanEtAl-ParameterEstimationinODE-ParticlaSwarmOptimimzationAkman, Devin, Olcay Akman, and Elsa Schaefer. 2018. Journal of Applied Mathematics.Volume 2018. pp 1-10.Abstract: Researchers using ordinary differential equations to model phenomena face two main challenges among...
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3-015-S-StyrofoamBallFall
24 Mar 2020 | | Contributor(s):: Brian Winkel
We are given data on a falling Styrofoam ball and we seek to model this motion.
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2008-DuranCaginalp-ParameterOptimization-DE-AssetPriceForecasting
23 Mar 2020 | | Contributor(s):: Brian Winkel
2008-DuranCaginalp-ParameterOptimization-DE-AssetPriceForecasting Duran, Ahmet and Gunduz Caginalp. 2008. Parameter optimization for differential equations in asset price forecasting. Optimization Methods and Software. 23: 551-574. Abstract: A system of nonlinear asset flow...
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2016-Langtangen-Pederson-ScalingDifferentialEquaitons
20 Mar 2020 | | Contributor(s):: Brian Winkel
2016-Langtangen-Pederson-ScalingDifferentialEquaitonsLangtangen, Hans Petter and Geir K. Pedersen. 2016. Scaling of Differential Equations. New York: Springer. Text 234 pages. https://www.springer.com/gp/book/9783319327259. Accessed 20 March 2020.The Preface,Finding proper...