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    2014-Vance-Eads-Sensitivity Analysis of a Three-Species Nonlinear Response Omnivory Model with Predator Stage Structure
    We investigate a three-species nonlinear response omnivory model incorporating stage structure in the top predator. The model consists of four coupled ordinary differential equations involving...

    Keywords: stage structuresensitivity analysismortalityomnivoreomnivory modelsearch rates

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    2012-Nokkaew-EtAl-Estimation of Algae Growth Model Parameters by a Double Layer Genetic Algorithm
    This paper presents a double layer genetic algorithm (DLGA) to improve performance of the information-constrained parameter estimations.

    Keywords: optimizationalgae growthgenetic algorithmssimulated dataconvergence of parameters

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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.

    Keywords: chemical engineeringsmoothing-based relaxation method

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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.

    Keywords: logisticpopulationparameciaGausegradient search

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    2010-Jungck-EtAl-Mathematical Manipulative Models-In Defense of Beanbag Biology
    This paper offers up samples of projects from the Bio- QUEST Curriculum Consortium’s 24-yr experience of holding faculty development workshops for biology and mathematics educators.

    Keywords: epidemiologysimulationinfectious diseasedisease transmissiondiseasein-class activitybean bag activity

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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.

    Keywords: kineticschemical kineticszeroth order reactionfirst order reactionsecond order reaction

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    2008-Brewer-EtAl-Fitting ordinary differential equations to short time course data
    In this paper, we present a survey of existing algorithms and describe the main approaches. We also introduce and evaluate a new efficient technique for estimating ODEs linear in parameters...

    Keywords: time seriesEvaluation SPLINEgeneleast squaresbifurcation

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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.

    Keywords: estimating equationfunctional data analysisGauss–Newton methodparameter cascadeprofiled estimationdynamic system

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    2007-Mogen_Steffensen-Differential Equations in Finance and Life Insurance
    The mathematics of finance and the mathematics of life insurance were always intersecting. Life insurance contracts specify an exchange of streams of payments between the insurance company and the...

    Keywords: financedisabilitylife insurancemortalityinsuraneThiele’s equationBlack-Scholes equation

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    2003-Givens-Bonfima-Direct observation of normal modes in coupled oscillators
    We propose a simple and inexpensive method to directly observe each normal mode of a system of coupled oscillators, as well as to measure its corresponding frequency, without performing Fourier...

    Keywords: frequencyresonancecoupled oscillator

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    2003-Bohren-Dimensional analysis-falling bodies--fine art of not solving differential equations
    Dimensional analysis is a simple, physically transparent and intuitive method for obtaining approximate solutions to physics problems, especially in mechanics.

    Keywords: falling bodydimensional analysisdrag

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    2000-Dwayne-Anderson-Estimates of the future membership of the Church of Jesus Christ of Latter-Day Saints
    Thus, the purpose of this paper is to model the membership of the Church of the Latter Day Saints from the available data on membership from 1844 to 2000.

    Keywords: population dynamicslogisticLatter-Day Saints

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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...

    Keywords: sum of square errorsleast squarespharmacokineticslineteicscompartmental modelsdirect search

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    1991-JR_Lobry-P_Flandois-Comparison of Monod's Growth Model Parameters from the Same Data Set
    The paper obtains the parameters in Monod's Growth model using a minimization of the sum of square errors with a given data set and obtains confidence intervals

    Keywords: Confidence intervalssum of square errorslinearizationgrowthModo Growth model

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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.

    Keywords: compartment modelpharmacokineticsnonlinear estimationone compartment model

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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.

    Keywords: kineticsparameter estimationlogisticchemical kineticschemical reaction

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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...

    Keywords: population modelparameter estimationpopulationparameter

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    2016-I-Liang_Chern-Mathematical Modeling_and_Ordinary_Differential_Equations
    We let the author's Table of Contents speak for itself.

    Keywords: differential equationsmodelingtextbook

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    2019-Fred_Brauer-The_Final_Size_of_a_Serious_Epidemic
    In an epidemic of a serious disease, there is likely to be behavioral response that decreases the epidemic size considerably.

    Keywords: epidemicfinal sizebehavioral responseSIER modelrelations

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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.

    Keywords: simulationparameter estimationshoppingfittingbehaviour

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