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Downloads
Views
Date
Relevance
Potential Scenario
155
views
77
downloads
0
comments
1992-John_Mathews-Bounded population growth-a curve fitting lesson
The purpose of this article is to present two methods for fitting the logistic curve to data supplied by the U. S. census bureau.
data
logistic
linearization
fitting
Modeling Scenario
429
views
119
downloads
0
comments
6-067-LotkaVolterra-ModelingScenario
This modeling scenario guides students through the process of fitting the Lotka-Volterra model of two differential equations to a real time series observational data. Students use the capabilities of R and R studio.
time series
data
competition
Lotka-Volterra
model fitting
prediction
gauseR
experimental
Potential Scenario
162
views
83
downloads
0
comments
2009-Su-EtAl-Fitting Compartmental Models to Multiple Dose Pharmacokinetic Data using SAS
In the case of a multiple dose study where subjects experience different dosing times, a superposition principle can be used to recursively account for each additional dose.
SAS
superposition
pharmacokinetics
compartmental models
multiple dose
Potential Scenario
200
views
73
downloads
0
comments
2017-D_Goulet-Modeling, Simulating, and Parameter Fitting of Biochemical Kinetic Experiments
In many chemical and biological applications, systems of differential equations containing unknown parameters are used to explain empirical observations and experimental data. The differential equations are typically nonlinear.
optimization
Biochemistry
sensitivity analysis
chromatography
mass action
cluster analysis
conservation laws
dimerization
estrogen receptor protein
Potential Scenario
155
views
87
downloads
0
comments
2015-Heiko_Enderling-Integrating experimental data to calibrate quantitative cancer models
For quantitative cancer models to be meaningful and interpretable the number of unknown parameters must be kept minimal. We focus on a tumor hierarchy of cancer stem and progenitor non-stem cancer cells.
cancer
tumor
fitting
agent-based
Potential Scenario
119
views
53
downloads
0
comments
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 particularly suited to situations where noise levels are...
time series
Evaluation SPLINE
gene
least squares
bifurcation
Potential Scenario
182
views
49
downloads
0
comments
2012-Transtrum-Qiu-Optimal experiment selection for parameter estimation in biological differential equation models
We explore the question to what extent parameters can be efficiently estimated by appropriate experimental selection.
experimental design
systems biology
Association & Data Fitting
reaction rates
decay rates
Potential Scenario
166
views
89
downloads
0
comments
2018-Akman-EtAl-Parameter Estimation in Ordinary Differential Equations Modeling via Particle Swarm Optimization
We demonstrate Particle Swarm Optimization efficacy by showing that it outstrips evolutionary computing methods previously used to analyze an epidemic model.
epidemic
Particle Swarm Optimization
optimize parameters
Potential Scenario
240
views
79
downloads
0
comments
2017-Floyd_Ballard-Dice Activities for DE Models
This document includes descriptions of four activities that are appropriate for a calculus or differential equations class, all using dice to motivate a differential equation model for a real-world scenario.
simulation
curve fitting
c
dice
collect data
class activities
analyze data
class activity
Potential Scenario
148
views
44
downloads
0
comments
2010-Singh-Mishra-athematical modeling approach to study growth rate of grassroots technological innovations
In this paper we have proposed a simple mathematical model by using ordinary differential equation to know the spread rate of technological innovations in rural India.
logistic
exponential
sigmoid
technological innovations
asymptotic
spread of innovation
Technique Narrative
424
views
206
downloads
0
comments
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 solutions may be obtained.
computation
error
Torricelli's Law
data fitting
linear approximation
Modeling Scenario
368
views
221
downloads
0
comments
1-005C-OilSlick-ModelingScenario
We describe a modeling activity for Calculus I students in which modeling with difference and differential equations is appropriate.
Problem Solving
oil slick
spread
fitting
line
assumptions
Modeling Scenario
255
views
222
downloads
0
comments
1-054-GrowthInFarmland-ModelingScenario
An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple...
fitting
farm
farmland
Modeling Scenario
253
views
218
downloads
0
comments
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.
data
logistic
population
Gompertz
census
goodness of fit
Modeling Scenario
1185
views
3704
downloads
0
comments
1-005-OilSlick-ModelingScenario
We describe a modeling activity with difference and differential equations which enlightens students on the model building process and parameter estimation for a linear, first-order, non-homogeneous, ordinary differential equation.
model fitting
spreadsheets
Spanish
derrame de petróleo
datos
expansión
oil slick
Modeling Scenario
377
views
441
downloads
0
comments
1-011A-Kinetics-ModelingScenario
We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction.
kinetics
Law of Mass Action
fitting
order of reaction
chemical reaction
Modeling Scenario
444
views
579
downloads
0
comments
1-011-Kinetics-ModelingScenario
We make the connection between chemistry course and differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and second order reactions.
kinetics
chemistry
Law of Mass Action
chemical kinetics
order of reaction
chemical reaction
Modeling Scenario
296
views
400
downloads
0
comments
3-060-DataToDifferentialEquation-ModelingScenario
Students use knowledge of second-order linear differential equations in conjunction with physical intuition of spring-mass systems to estimate the damping coefficient and spring constant from data.
Association & Data Fitting
mass
spring-mass system
spring\
total distance
numerical differentiation
Modeling Scenario
223
views
255
downloads
0
comments
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 tumor growth over time.
Pop_Growth Pilot
logistic
comparment
tumor
synthetic data
sum of squares error
Potential Scenario
136
views
80
downloads
0
comments
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 method to estimate mixed-effects ODE models.
pharmacokinetics
dynamic models
smoothing
spline
mixed-effects models
HiV combination therapy
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