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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...

    Keywords: pharmacokineticsdynamic modelssmoothingsplinemixed-effects modelsHiV combination therapy

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    2014-Michael_Monagan-The Mortgage Payment Problem Approximating a Discrete Process with a Differential Equation
    In this article and a subsequent article I will give two non-standard examples that I've found helpful. The one presented here is a first order linear system. Second order systems and non-linear...

    Keywords: compartmentheatinghouse

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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...

    Keywords: Saccharomyces cerevisiaelogisticyeastdeathgrowthsugaralcohol

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    2012-Shargel-Yu-AccessPharmacy-Applied Biopharmaceutics and Pharmacokinetics
    Step by step formation of drug absorption models is shown with many good graphics of system and plots. Solutions are offered but no solution methods are shown.

    Keywords: Michaelis-MentenEnzymesubstratecompartmentpharmacokineticsrate constanturinary dataabsorption rate

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    2012-José_Sérgio_Domingues-Gompertz Model - Resolution and Analysis for Tumors
    The main objective of this paper is to use the Gompertz equation in order to study the development of blood irrigated solid tumors, using parameters defined in some important bibliographic...

    Keywords: tumorGompertz equationgrowth tumor

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    2011-Kenny_Harwood-Modeling a RLC Circuit Current with Differential Equations
    This paper gives an abbreviated description of the photovaltaic effect (solar power production process) and then a RLC circuit will be modeled that is powered by a photovaltaic panel.

    Keywords: tuningfrequency responseLC circuitRLC

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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-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...

    Keywords: longitudinal dataAIDSantiretroviral drug therapyBayesian nonlinear mixed-effectstime-varying drug efficacyHIV dynamics

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    2008-Duran-Caginalp-Parameter optimization for differential equations in asset price forecasting
    The optimization procedure is used in conjunction with daily market prices (MPs) and net asset values to determine the parameters for which the AFDE yield the best fit for the previous n days.

    Keywords: financeinverse problemnumerical nonlinear optimizationasset flowfinancial market dynamicsmarket return prediction algorithm

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    2007-Zenker-Rubin-Clermont-From inverse problems in mathematical physiology to quantitative differential diagnoses
    The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data...

    Keywords: physiologyinverse problem

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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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    Engaging Students in Pharmacogenetics: Patient Case Studies Using the PharmGKB Website
    Cytochrome P450 (CYP) enzymes are important regulators of drug efficacy and toxicity. Genetic variation in CYP isoforms can impact how well patients respond to medications or experience unwanted...

    Keywords: toxicologyPharmacologydrug metabolismpharmacodynamicspharmacogenetics

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    2006-Cooke-Elderkin-Huang-Predator-Prey interactions with delays due to juvenile maturation
    This paper focuses on predator-prey models with juvenile/mature class structure for each of the predator and prey populations in turn, further classified by whether juvenile or mature individuals...

    Keywords: predator-preyhost-parasitebifurcationage structrematuration delay

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    Discovery and Invention: A Reflection on Representation in Science
    Despite increased awareness of the lack of equity and inclusion in the STEMM classroom, lessons on DEI topics are treated as separate to the scientific curriculum being taught. Rarely are...

    Keywords: EquityDiversity and Inclusionantiracism

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    2005-Saifullah-Mathematical Modeling With Differential Equations
    This article aims to provide the students some basic modeling skills, which will have applications to a wide variety of problems.

    Keywords: species interactionsword equationinteractive software

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    2005-Minna_Wedenberg-Pharmacokinetic modeling of gastric emptying
    The development of new drug substances is a complex, time consuming and expensive process. Reducing the time for drug development and avoiding late termination of candidate drugs are important...

    Keywords: paracetamolpharmacokineticsstomachsmall intestinesulfapyridine

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    2004-Hill-Lozowski-Sampson-Experiments on ice spikes and a simple growth model
    We observed ice-spike growth using time-lapse digital photography, using two water types in two different containers.

    Keywords: iceice spikebulk heat transfermass conservation

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    Who’s That Speci-Mon? Using PokémonTM to Understand Biological Terminology Using Greek and Latin Roots
    We set out to create a fun and engaging activity using recognizable fictional characters, so students get a chance to practice using Greek and Latin roots to create binomial names. Students in...

    Keywords: linguisticstaxonomyAnatomyGreek and Latin Roots

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    2003-Yildirim-Mackey-Feedback Regulation in the Lactose Operon
    A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented.

    Keywords: mRNAlactoselactose operonfeedback regulation

    159

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