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    2017-Bonin-EtAl-Mathematical modeling based on ordinary differential equations - promising approach to vaccinology
    As a proof of concept, we developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data...

    Keywords: immune systemyellow fevercomputational immunologycomputational vaccinology

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    2017-Adolfo_Rumbos-Differential Equations and modeling
    The study of any phenomenon in the physical or biological sciences, in which continuity and differentiability assumptions about the quantities in question can be made, invariably leads to a...

    Keywords: pendulumLotka Volterra equationsexistenceuniqueness

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    The Leaky Neuron: Understanding synaptic integration using an analogy involving leaky cups
    Students have difficulty understanding synaptic integration in neural circuits, and how spatial and temporal summation combine in a target neuron to reach threshold.  This Lesson uses small...

    Keywords: neuron physiologyspatial summationsynaptic integrationtemporal summationthreshold

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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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    2003-Givens-Bonfima-Direct observation of normal modes in coupled oscillators
    We propose a simple and inexpensive method to directly observe each normal mode of a system of coupled oscillators, as well as to measure its corresponding frequency, without performing Fourier...

    Keywords: frequencyresonancecoupled oscillator

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    1991-Carmine_Chicone-Ordinary Differential Equations with Applications
    This is a complete text for a graduate level course. Hence there is much theory, but there is a chapter on applications with some sophisticated approaches and high level modeling of motion.

    Keywords: orbitstwo mass systematommagnetic fieldcoupled penduluminverted pendulumcharged particleKepler motion

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    2019_Isaac_Eshakoff-Differential_Equations_of_Love_and_Love_of_Differential_Equations
    In this paper, simple ordinary differential equations are discussed against the background of William Shakespeare’s Romeo and Juliet.

    Keywords: mathematical modelsystemmechanicalRomeo and Julietlovelove-hatejealousyShakespeare

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    3-010-EnergyInSpringMassSystem-ModlingScenario
    As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring...

    Keywords: energymass-spring systemkinetic energypotential energytotal energy

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    2016-Bonin-EtAl-Mathematical modeling based on ordinary differential equations-vaccinology
    We developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature.

    Keywords: Immunologyimmune systemAntigenvaccinologyyellow fever

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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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    2007-Joseph_Myers-Brian_Winkel-Modeling_a_Mystery_Circuit_in_Mathematics_Class_Using_Differential_Equations_Laplace_Transforms_and_Transfer_Functions
    We discuss the introduction, student discovery, and teaching of a system of differential equations which model a circuit.

    Keywords: circuitLaplace transformtransfer functionmystery circuitvoltage frequencytwo loop circuit

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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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    2018-Kovacs-Insperger-Retarded neutral and advanced differential equation models for balancing using an accelerometer
    It is shown that slight modeling differences lead to significant qualitative change in the behavior of the system, which is demonstrated by means of the stability diagrams for the different models.

    Keywords: feedbackAccelerometersfunctional differential equationssemi-discretizationD-subdivision method

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    2012-Rusinko-Swan-Agent-Based Fabric Modeling Using Differential Equations
    We use an agent-based modeling software, NetLogo, to simulate fabric drape by applying a modified mass spring system.

    Keywords: NetLogospring massagent-baseddrapingyarnfabric

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    2004-Jones-Song-Thomas-Controlling wound healing through debridement
    In this article, a system of differential equations that models slough/wound interaction is developed.

    Keywords: bacteriawound healinghealingderidingisocline

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    A Simple Method for Predicting a Molecule's Biological Properties From Its Polarity
    The distinction between very polar and less polar substances is a foundation of biochemistry, cell biology, and physiology; it surfaces in multiple concept inventories and elaborations of...

    Keywords: Diffusionsolubilitycovalent bondshydrophilichydrophobicpartition coefficientplasma membranepolarity

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    Isolation and Functional Analysis of a Pancreatic Enzyme in an Introductory Student Lab
    Structure and function are correlated at all levels of biology. This topic is typically addressed early in an undergraduate class in general or molecular biology before students have gained much...

    Keywords: Protein StructureproteaseEnzymechemical bondscatalysissolubility

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    2016-Barbarossa-Kuttler-Mathematical Modeling of Bacteria Communication in Continuous Cultures
    This paper presents a simple system of delay differential equations (DDEs) for quorum sensing of Pseudomonas putida with one positive feedback plus one (delayed) negative feedback mechanism.

    Keywords: gene regulatory networkschemostatbifurcationNumerical Simulationquorum sensing

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    2010-Shianga-EtAl-Computational model of the human glucose-insulin regulatory system
    A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced. The

    Keywords: glucose tolerance testsum of squared residualsmultiple shooting methodcost function

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    2019-Banuelos_Danet_Flores_Ramos-Epidemiological_Math_Model_Approach_To_Political_System_with_Three_Parties
    A nonlinear compartmental model is derived to study the movement between classes of voters with the assumption of a constant population that is homogeneously mixed.

    Keywords: politicsparametersvotingcompartment modelepidemiological modelequilibriathree-party system

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