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    2016-Langtangen-Pedersen - Scaling of Differential Equations
    Nowadays, the greatest practical benefit of scaling is related to running numerical simulations, since scaling greatly simplifies the choice of values for the input data and makes the simulations...

    Keywords: scalingdimensionlesscontinuum mechanics

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    Why Cells Change Weight: Demonstrating Linear Regression Through an Osmosis Experiment
    In this activity, students will perform an experiment utilizing dialysis tubing to create cellular models to demonstrate the linear relationship between cell weight and time in varying tonicities....

    Keywords: graphingqbccCellular and Molecular BiologyInterpret graphsConcepts in Statistics

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    Module M.5 Linear mixed-effects models
    Introduction to Primate Data Exploration and Linear Modeling with R was created with the goal of providing training to undergraduate biology students on data management and statistical analysis...

    Keywords: R programming languageprimatespopulation ecology

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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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    Making Predictions with Linear Models: A Murder Mystery Case Study
    This Swirl lesson will introduce two main concepts to students: 1) the idea of uncertainty around linear slopes versus individual values and 2) predicting values using linear models.

    Keywords: data visualizationlinear modelscase study teachinguncertaintypredictionConfidence intervals

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    6-006-ZombieGameHvZ-ModelingScenario
    Invented in 2005, Humans vs. Zombies, or HvZ, is a game of tag, predominantly played at US college campuses. In this activity, students use systems of non-linear differential equations to model...

    Keywords: zombiesSIR modelsGame

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    The Influence of Exotic Plant Invasion on Pollinator Abundance
    This lesson introduces two global change factors, natural habitat loss and exotic plant invasion, and analyzes how these stressors impact the biodiversity and abundance of pollinator species....

    Keywords: statisticsinvasion biologyecologyRStudioBiodiversityInvasive SpeciesPearson correlation coefficientgeneral linear modelsinvasive plantspollinatorsPopulation abundance

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    Module M.4 Simple linear regression analysis
    Introduction to Primate Data Exploration and Linear Modeling with R was created with the goal of providing training to undergraduate biology students on data management and statistical analysis...

    Keywords: R programming languageprimatespopulation ecology

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    1-098-NeuronDetection-ModelingScenario
    Students study a linear, first order, one-dimensional ordinary differential equation (ODE) and learn how it can help understand basics of neural dynamics. The modeling framework is known in ...

    Keywords: biologyneuroscienceneuron physiologyvoltageintegrate and firethrefholscoincidence detectionRC circuit

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    2014-Blomhøj-EtAl-Compartment models
    An overview of compartment models with many rich illustrations and much attention to various numerical methods in solutions of the resulting differential equations using Matlab. Also included is a...

    Keywords: concentrationkineticsphysiologycompartmentsalttankbalancereactionsminkbathtub

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    2015-Sivakumar-EtAl-Approximate Analytical Expression of Concentrations in a Kinetic Model for Biogas Generation from Banana Waste
    The initial value problem in a kinetic model for biogas generation from banana waste is discussed. The model involves the system of non-linear differential equations which has variety of non-linear...

    Keywords: chemical kineticsMichaelis-Menten kineticsanaerobic digestionacidogenic stepsbananamethanogenic stepswastes

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    Enzyme Kinetics: How Quickly Can Acetylcholinesterase Break Up Your Thoughts?
    This module contains exercises designed to help upper-level cell biology students understand the common graphical methods used to evaluate enzyme activity and to see the impact of inhibitors on...

    Keywords: cell biologyQuantitative reasoninginterdisciplinarylinear modelsInterpreting GraphsNIQBC2. Data and GraphsC4. mathematical modelsnonlinear models

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    2015-Jonathon_Easton, Jonathan-Mathematical models of health focusing on diabetes-Delay differential equations and data mining
    This is an exhaustive study with very good references of a linear system of four differential equations with and without delay to model diabetes in a human being.

    Keywords: diabeteshealth model

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    1-109-EmployeeAttrition-ModelingScenario
    This scenario models the loss of employees and the employer's attempt to retain them through stock options. It most naturally is solved with a first-order linear decay model with two populations.

    Keywords: populationlinear growthdecayemployeeattrition

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    1-114-EarthClimate-ModelingScenario
    In this modeling scenario, we investigate the Earth's climate using a zero-dimensional energy balance model. Energy balance models are climate models that try to predict the average surface...

    Keywords: climateenergytemperaturelinearizationphase linesenergy balance modelroot finding

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    Linear Regression (Excel) and Cellular Respiration for Biology, Chemistry and Mathematics
    Students typically find linear regression analysis of data sets in a biology classroom challenging. These activities could be used in a Biology, Chemistry, Mathematics, or Statistics course. The...

    Keywords: statisticsmathematicsdata analysisdatalinear regressionbiologyonlinegraphinglinear equationsQuantitative reasoningassessmentcollege algebracellstatistical analysisregressionOERAlgebrachemistryModelscorrelationSimple Linear RegressionMicrosoft Excellab activityexperimentCellular ProcessesATPqbccUsing Excelmanipulate equationsCellular and Molecular BiologyConcepts in Statisticsoxidationline of best fitexplaining statisticsusing statisticsCellular RespirationPredictionsRespirationgraphing in ExcelLinear CorrelationExothermic Reactioncreate scatter plotAdenosine Triphosphate (ATP)germinating peasPre-lab activityStudent activityHybridCollecting DataR-squareRegression ModelFunctionDependent VariablesIndependent VariablesLinear EquationLinear Equation in two variablescreate graphcreate equationcreate regressioncreate plotinterpret regressioninterpret data

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    1981-Nielsen_Francois-Rachel_Rosenfeld-Substantive_Interpretations_of_Differential_Equation_Models
    The interpretation of parameters of dynamic models is illustrated with reference to research on two substantive topics: political mobilization and intragenerational mobility.

    Keywords: differential equationsdynamical systemsFirst order linearintragenerational mobilitypolitical mobilizationmobility

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    2014-Allen-EtAl-Perturbations in Epidemiological Models -When zombies attack we can survive
    In this paper, we investigate the existence of stability-changing bifurcations in epidemiological models used to study the spread of zombiism through a human population.

    Keywords: epidemiologydynamical systemszombiesbifurcationperturbation

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    2001-A_Tsoularis-Analysis_of_logistic_growth_models
    The paper presents an historical development of the logistic equation in its various forms, including Verhulst, Pearl and Reed, Gompertz, Bertalanffy, Richards, and others.

    Keywords: logisticpopulationgrowth curvelimited growthGompertzhistorylogistic equationVerhulstPearl and ReedBertalanffyRichards

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    5-010-DNADegradation-ModelingScenario
    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...

    Keywords: DNA\kinetisplasmaratpharmacokinetis

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