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DEDiscover Differential Equation Modeling Solution. CANGLIN WU June-18-2007. DEDiscover Differential Equation Modeling Solution. - PowerPoint PPT Presentation
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DEDiscoverDifferential Equation Modeling Solution
CANGLIN WUJune-18-2007
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
DEDiscover is a cross-platform software tool for building and understanding differential equation models, with special attention to the features necessary for modeling the immune system and viral infection.
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
General Features• Cross-platform: Windows, Linux
and Mac OS • Import models and export
standard data and image formats (e.g. CellML, SBML, PNG, JPEG, PS, EPS etc.)
• Plug in architecture
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
Model Support• Standard mathematical notations,
plus macros, indicator functions, time-varying parameters, history functions, and constraints
• ODE and DDE models• Pre-defined or user specified models
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
Model input and solver selection
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling olution
Parameters and initial conditions
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
Simulation Support• Several ODE and DDE solvers• Real-time solutions allow
interactive exploration• Tabular and Graphical display
of results • Customizable displays
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
Simulation result - Combined plot
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
Simulation result - Individual plot
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
Simulation result - Table
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
Estimation Support • Several estimation & optimizer methods• Point estimates and confidence intervals • Estimation of both initial conditions and
parameters• Properly fits data with experiment,
treatment, and technical replicates• Interactive display and control of
estimation progress
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
Formula Syntax• Dependent variable, dEP/dt• Delay variable, TE(t-tau_T)• Temporary variable like MACRO,
suggest use temp_ as prefix, for example temp_var= k*T1*V• Suggest capital for variable and low-
case for parameter
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
Formula Syntax
• Indicator functionI(tau_T,100)(t) tau_T<I<100I[tau_T,100)(t) tau_T<=I<100I(tau_T,100](t) tau_T<I<=100I[tau_T,100](t) tau_T<=I<=100• Initial condition in formula, D(0) • Comment, // for comment one line, /* */ for
comment multiple lines
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
Formula Syntax• Case insensitive, V and v are same
variable NOT two variables• DO NOT use * as a part of variable
name, reserved for multiple operation
• DO NOT use T or t as variable name, reserved for independent variable
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
Reserved Words• T, t, //, /*, */, + , - , * , / , = , , , . ,
( , ) , < , > , ‘ , ^ , e , log , sin , cos , tan etc
• You CAN NOT use reserved word as variable and parameter name
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
Operator• + Add• - Subtract• * Multiply• / Divide• % Modulus • ^ Power: y = x ^ 2( ) • () Parenthesis. For example: (2 + 3) * 5
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
Math functions• sin(x) Calculate sine• sinh(x)Calculate hyperbolic sine• Cos(x) Calculate cosine • Cosh(x) Calculate hyperbolic cosine• tan(x) Calculate tangent• tanh(x) Calculate hyperbolic tangent• asin(x) Calculate arcsine • acos(x) Calculate arccosine• atan(x) Calculate arctangent• atan2(x, y) Calculate arctangent with two parameters to preserve
quadrant angle• bessj(n, v) Bessel function of the first kind. n isorder and v is input
value.• bessy(n, v).Bessell function of the second kind. nis order and v is
input value• hypot(a,b) Calculate hypotenuse of right triangle
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
Math functions• abs(x) Return absolute value• max(x) Return larger of two values• min(x) Return smaller of two values• sqrt(x) Find square root• Ceil(x) Find integer ceiling • floor(x) Calculate hypotenuse of right triangle• exp(x) Calculate exponential function: ex• log(x) Calculate natural logarithm• log10(x) Calculate base-10 logarithm• rand(x) Get pseudorandom number between 0 and 1• srand(x) Initialize pseudorandom series
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
Download • Log in CBIM website first • Download at
http://cbim.urmc.rochester.edu/software
• Install DEDiscover package in your computer
June-18-2007 2007 Pittsburgh Workshop Canglin Wu
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DEDiscoverDifferential Equation Modeling Solution
DEDicover DEMO
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DEDiscoverDifferential Equation Modeling Solution
Acknowledgment• NIAID/NIH grant NO1 AI50020Center for Biodefense Immune Modeling • Design : Hulin Wu, Gregory Warnes,
Dongwen Wang• Program: Hongyu Miao, Alain Leblanc• Model: Alan Perelson, HY Lee, SY Lee• Other: Jeanne Holden-Wiltse, Temple
Herlong
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DEDiscoverDifferential Equation Modeling Solution
ThanksQ & A