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    3D breast cancer tissue reconstruction
    This module allows students to follow a researcher as she discovers new features of breast cancer tissue architecture, using 3D reconstructions of histological specimens.

    Keywords: graphingdata visualizationbreast cancerDCIShistogramscentroidsums of squares

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    Math Bench Probability and Statistics: Mice with Fangs - Intro to Punnett Squares
    This is an online activity that provides an introduction to Punnett squares as a tool for visualizing genetic inheritance. The ratios of possible genotypes and phenotypes in offspring are...

    Keywords: geneticsResources @ MathBenchonlineMathBenchpunnett squares

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    More Mice with Fangs: Intermediate Punnett Squares
    An online module utilizing probability and Punnett squares to introduce students to more complex genetic problems. The module emphasizes students' use of probability to solve the problems.

    Keywords: geneticsProbabilityResources @ MathBenchonlinepunnett squares

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    Linked Genes and Recombination: Advanced Punnett Squares
    An online module in which students learn about more difficult genetics problems, including linked genes and crossing over. Quantitatively students learn about marginal probabilities and chi-square...

    Keywords: geneticsProbabilityResources @ MathBenchonlinepunnett squareslinked genes

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    2015-Carl_Lutzer-Using Expected Value to Introduce the Laplace Transform
    We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at...

    Keywords: Expected ValueRiemann sumnet change

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    2015-Zhang-EtAl-On the Selection of ODE Models with Application to Predator-Prey Dynamical Models
    We propose a computationally inexpensive approach that employs statistical estimation of the full model, followed by a combination of a least squares approximation (LSA) and the adaptive Lasso.

    Keywords: least-squares approximationSpline modelingMonte Carlo simulationsvariable selectionadaptive LASSO

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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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    Spreadsheet Tutorial 2 - Autofill Data, Cell References, and Standard Deviation
    Generate a table with autofill, and use absolute cell reference to calculate variance and standard deviation.

    Keywords: Resources @ HHMI - BioInteractiveScientific ProcessStatistics and MathScientific MethodologyHigh School

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    Investigating the Drivers of Western Monarch Decline Using Partial Least Squares Regression
    In this lesson, students will explore the drivers of the western monarch butterfly decline. Students will compare the effects of climate factors and land use factors on the western monarch...

    Keywords: RStudiomultivariate analysisMonarch butterfliesPartial Least Squares Regression

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    Data Visualization
    This is an introduction to the idea of data visualization and the importance of presenting data for understanding.

    Keywords: data in the classroomdata visualization

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    A Direct Experience Study of Density-Dependent Growth
    An experiential approach to density-dependent growth using a checkerboard, 6-sided die, and two types of markers.

    Keywords: logistic growthdensity dependenceexperiential

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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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    8-002-TrigSumRepresentation-TechniqueNarrative
    Students discover how to represent functions as sums of trigonometric functions and the value of such representations in many fields. This is an introduction to the study of Fourier Series.

    Keywords: estimationTrigonometryTrigonometric Functionssum of square errorsfinite sumFourier seriesFouriere sumspectrumapproximatiopn

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    Working with plant phenology data and fitting a nonlinear model using least squares in R
    A participatory live-coding lesson on working with NEON phenology data and fitting a sine-wave model to determine when different species get and lose their leaves.

    Keywords: modelingRphenologyNEONRstatscodeparticipatory live-coding

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    1987

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    Striped Bass: A Regulatory Success Story
    This module examines the Maryland striped bass moratorium (1985-1989) as a fisheries management success story. Maryland DNR striped bass young of the year data is utilized for least squares linear...

    Keywords: regressionfisheriesmonitoringrecruitmentstriped bassmoratoriumfish biologyfisheries ecologyspawninganadromousyoung of the yearrelative abundancechesapeake bayfish population

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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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    2017-Justin_Krueger-Parameter Estimation Methods for Ordinary Differential Equation Models with Applications to Microbiology
    We demonstrate the feasibility of principal differential analysis using simulation studies and then apply the method to intestinal and vaginal microbiota data.

    Keywords: microbiologyLotka Volterrramicrobiota

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    1-066-USCensusModeling-ModelingScenario
    The United States Census, conducted every 10 years, gives data on the United States population, that can be modeled with the exponential, logistic, or Gompertz functions.

    Keywords: datalogisticpopulationGompertzcensusgoodness of fit

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    6-029-TumorGrowth-ModelingScenario
    This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of...

    Keywords: Pop_Growth Pilotlogisticcomparmenttumorsynthetic datasum of squares error

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    2013-Fathalla_Rihan-Delay Differential Equations in Biosciences - Parameter estimation and sensitivity analysis
    This is a review article to show that delay differential models have a richer mathematical framework (compared with models without memory or after-effects) and a better consistency with biological...

    Keywords: epidemiologysensitivityImmunologyphysiologyRK-methodstime-lags

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