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    A Hands-on Introduction to Hidden Markov Models
    In this Lesson, we describe a classroom activity that demonstrates how a Hidden Markov Model (HMM) is applied to predict a eukaryotic gene, focusing on predicting one exon-intron boundary. This HMM...

    Keywords: transcriptionexonintronsplicing

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    2018-Adeniji-EtAl-InverseProblemHolling-TannerModel
    We consider the inverse problem of parameter identification of nonlinear system of ODEs for a specific case of complete information about solution of the Holling-Tanner model for finite number of...

    Keywords: goal functionabsolute error curvesinvers methodholling-Tanner model

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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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    2018-Weber_Theers_Surmann_Ligges_Weihs-Sensitivity Analysis_of_Ordinary_Differential_Equation_Models
    This report will focus on the sensitivity analysis of ordinary differential equation (ODE) models since they can be used to model so-called Low Frequency Oscillations (LFOs).

    Keywords: sensitivityregressionparameter estimationsystemlow frequency oscillationsoscillations

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    2014-John_Cimbala-Dynamic System Response
    In this learning module, we discuss the dynamic system response of sensors and their associated electronic circuits.

    Keywords: sensor networksoscillationssystem responseelectronic circuit

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    1999-Meyer-Ausubel-Carrying Capacity-A Model with Logistically Varying Limits
    This paper extends the logistic equation to simple growth model with a logistically increasing carrying capacity. This is applied to human population situations in several countries with fits to data.

    Keywords: population dynamicsparameter estimationlimited growthgrowthlogisitic

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    2015-Brian_Winkel-Informed_Conjecturing_of_Solutions_for_Differential_Equations_In_a_Modeling_Contex
    We examine (1) first order exponential growth or decay and (2) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a...

    Keywords: exponential growthsolutionslinear systemsdecayconjecture

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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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    1-135-FishHarvesting-ModelingScenario
    This short activity will walk students through a guided list of questions to help them to understand how the stability of equilibrium changes with changes in a model parameter, in this case the...

    Keywords: population dynamicsfishstabilitybifurcationharvest

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    1-018-LogisticPopModel-ModelingScenario
    We offer artificial (toy) and historical data on limited growth population situations in the study of protozoa and lead students through several approaches to estimating parameters and determining...

    Keywords: data analysisparameter estimationlogisticCiliate protozoapopulationlimited growthparameciaGause

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    The Stomata Lab. What the past can tell us about our future - using fossil and modern plants to model atmospheric carbon dioxide
    Students will develop a mathematical model of the relationship between atmospheric CO2 and the number of stomata on a leaf (Stomata Index). They will evaluate the model graphically, statistically,...

    Keywords: introductory biologyQuantitative reasoninginterdisciplinaryclimate changeregressionEcology and EvolutionStomataNIQBC2. Data and GraphsC4. mathematical modelsC3. Statistical AnalysisSmithsonian

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    1984-W_Brunner-D__Focht-Deterministic Three-Half-Order Kinetic Model for Microbial Degradation
    The kinetics of mineralization of carbonaceous substrates has been explained by a deterministic model which is applicable to either growth or nongrowth conditions in soil.

    Keywords: kineticsnonlinear regressionsum of square errorsMonodlinearizemineralizationsubstratescarbonaceous

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    2017-Sim-EtAl-Optimal control of a coupled tanks system with model-reality differences
    In this paper, an efficient computational approach is proposed to optimize and control a coupled tanks system.

    Keywords: optimal controlflowtankscoupled tanks

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    1968-Wagner-Aghajanian-Bing-Correlation of performance test scores with tissue concentration of lysergic acid diethylamide
    This paper offers a two compartment model of lysergic acid diethylamide (LSD) in volunteer students and through parameter estimation models the amount of LSD in the tissue after its initial...

    Keywords: LSDcorrelation coefficientcompartment modellysergic acid diethylamideperformancetest scoretissue concentration

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    4-023-MysteryCircuit-ModelingScenario
    Students to build a system of differential equations which model a circuit. We give each student a unique input voltage frequency parameter and ask for system response (gain) to that input as a...

    Keywords: filterscircuitRLC circuitKirchhoffvoltagegaindriver

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    Angiosperm Diversity in Pollination Systems
    This activity is designed for upper-level undergraduates and graduate students engaged in ecology and biodiversity sustainability studies. This activity will explore how plant-pollinator...

    Keywords: data visualizationBiodiversityplantsPlant-insect interactionsnetworkinsectsBLUEpollinators

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    2006-Han-EtAl-Ordinary differential equation models for ethanol pharmacokinetic based on anatomy and physiology
    Physiologically-based pharmacokinetic (PBPK) models have been used to describe the distribution and elimination characteristics of intravenous ethanol administration.

    Keywords: liverwortsintraveneouspharmacokineticsethanolethanol infustionpharmacodynamictissue model

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    Plate Tectonics: GPS Data, Boundary Zones, and Earthquake Hazards (Project EDDIE)
    Students work with high precision GPS data to explore how motion near a plate boundary is distributed over a larger region and hypothesize the area over which boundary-related earthquake hazards...
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    Population Ecology in Swirl: Estimating Population Sizes
    The students will learn to estimate population sizes and consider assumptions of mathematical models and their applicability to the ecology of an organism/population

    Keywords: RSwirl

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    State Apportionment Lesson Plans and Task
    Three secondary teachers and a mathematics education researcher planned two lessons and revised them through lesson study. The teachers adapted the State Apportionment Task from the Mathematical...

    Keywords: votingproportional reasoning

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