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    2014-Enderling-Chaplain-Mathematical Modeling of Tumor Growth and Treatment
    Herein we describe fundamentals of mathematical modeling of tumor growth and tumor-host interactions, and summarize some of the seminal and most prominent approaches.

    Keywords: cancertumor modelingangiogenesistumor growthpatient care

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    2017-Alex_Honchar-Neural Networks For Solving Differential Equations
    In this post I want to show how I applied simple feed-forward NNs to different differential equations with increasing complexity: ODEs, second order ODEs, and, finally, PDEs.

    Keywords: neural networksCybenko theoremdiffusion equationfluid dynamics

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    6-002-EulerCromerPendulum-ModelingScenario
    This activity introduces students to the concept of numerical stability. While modeling a simple pendulum, students compare performance of the semi-implicit Euler-Cromer method with Euler's method...

    Keywords: pendulumsemi-implicit methodsEuler-Cromernumerical solvers

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    2003-Knorrenschild-Gross-Text Books on Mathematical Modeling in Biology
    Text Books on Mathematical Modeling in Biology Compiled from the Internet by Michael Knorrenschild,

    Keywords: biologyMathematical Biologytextbooktext

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    Quantitative reasoning: Interdisciplinary STEM 21st century reasoning modality
    Resource from the 2015 BioQUEST Summer Workshop

    Keywords: stemQuantitative reasoning

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    Fitting Exponential and Logistic Growth Models to Bacterial Cell Count Data
    In this activity, students will model a noisy set of bacterial cell count data using both exponential and logistic growth models. For each model the students will plot the data (or a linear...

    Keywords: modelingdata analysislinear regressiongraphingExponentsoptimizationcalculusInterpreting GraphsFunctionsqbccCellular and Molecular BiologyChoosing modelsUnderstanding ratesConcepts in Statisticsmeasurementsmanipulating equationscreating graphsExponential and Logarithmic Functionsinterpreting tables

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    Moths and Frogs and E. coli, Oh My!: Agent-based Modeling of Evolutionary Systems
    In evolution classrooms, introducing and reinforcing the idea of genetic drift and random selection can be challenging, as can be reinforcing appropriate mental models of evolution. Agent-based...

    Keywords: modelingEvolutionecologyagent-based modelingGenetic Driftenvironmental scienceNatural Selectioncompetitive coevolutionsimulation modelingevolutionary reasoning

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    2009-Noakes-Sleigh-Mathematical models for assessing the role of airflow on the risk of airborne infection in hospital wards
    Understanding the risk of airborne transmission can provide important information for designing safe healthcare environments with an appropriate level of environmental control for mitigating risks.

    Keywords: infectioncompartmenthospitalventilationairbornesthochasticWells–Riley

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    A Hands-on Introduction to Hidden Markov Models
    A lesson in which students will understand the basic structure of an HMM, the types of data used in ab initio gene prediction, and its consequent limitations.

    Keywords: Markov modelbioinformaticsgenomicsNIBLSEtranscriptionCourseSourceexonintronsplicing

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    2-005-LinearizeItAll-TechniqueNarrative
    Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form...

    Keywords: computationerrorTorricelli's Lawdata fittinglinear approximation

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    Central Dogma, Dictionaries, and Functions: Using Programming Concepts to Simulate Biological Processes
    Technologies like next-generation sequencing, proteomics, and high-throughput phenotyping have transformed the way we do biology. There is a continued need for scientists with computational skills...

    Keywords: computationpythonJupyter notebookFunctionscentral dogmaDictionaries

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    Using computational molecular modeling software to demonstrate how DNA mutations cause phenotypes
    Students require a deep understanding of the central dogma before they can understand complex topics such as evolution and biochemical disorders. However, getting undergraduate biology students to...

    Keywords: Protein Structurecomputational modelingcentral dogmaplant leaf structurePhenotype/Genotype

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    Diseasebots
    This module explores the effects of host density on contact rates and transmission of pathogens or mutualist symbionts using a hands-on simulation, a computer agent-based model in NetLogo, and an...

    Keywords: NetLogoDisease ecologydensity dependenceSpreadsheethost-parasitemutualismOpen-inquiry group projectsmanipulative models (‘beanbag biology’)plotting

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    Discovering Prokaryotic Gene Regulation by Building and Investigating a Computational Model of the lac Operon
    The ability to construct and reason through a biological system is an important skill to develop in science education. This level of understanding forces students to recognize the interrelatedness...

    Keywords: prokaryotesgene regulationLac Operoninducible operon

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    High technology to measure forest carbon stocks: How can advanced remote sensing improve biomass quantification in the Brazilian Amazon?
    A case study on the estimation of aboveground biomass using advanced remote sensors (LiDAR and hyperspectral) in the Brazilian Amazon. Students explore remote sensing (RS) data and compare RS-based...

    Keywords: climate changeremote sensinghyperspectraltropical forestsLiDAR data analysiscarbon stocks

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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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    1-030-RandomPerturbation-TechniqueNarrative
    After a brief historical view of this problem, we will demonstrate the derivation of first order linear differential equations with random perturbations.

    Keywords: random perturbationBrownian motionLangevin equationRiemann-Steiltjes integralWiener processIto's calculus

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    ModelSim Population Biology Unit
    This resource provides rich student modeling activities and materials, teacher resources, and much more, in the realm of agent based models applied to population biology.

    Keywords: modelingsimulationmoduleEvolutioncase studycurriculumagent-based modelpopulation modeldemonstrationin-class activityPresentation

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    2017-Rosario-Antony-Mathematical Model for Future Population Scenario In India And China – An Econometric Approach
    A mathematical model including dynamical systems, statistical models and differential equations involves variety abstract structures. Population growth is one of the main issues in India and China...

    Keywords: logisticIndiavital coefficientsAsiaCarrying Vapacitiyannual growth rate

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    2006-Wilensky-Reisman-Thinking Like a Wolf a Sheep or a Firefly
    We describe a computation-based approach that enables students to investigate the connections between different biological levels using agent-based, embodied modeling tools.

    Keywords: simulationNetLogopredator-preyagent-basedwolffox

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