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DEDiscover Differential Equation Modeling Solution

DEDiscover Differential Equation Modeling Solution. CANGLIN WU June-18-2007. DEDiscover Differential Equation Modeling Solution.

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DEDiscover Differential Equation Modeling Solution

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  1. DEDiscoverDifferential Equation Modeling Solution CANGLIN WU June-18-2007

  2. DEDiscoverDifferential Equation Modeling Solution DEDiscover is a cross-platform software tool for building and understanding differential equation models, with special attention to the features necessaryfor modeling the immune system and viral infection. 2007 Pittsburgh Workshop Canglin Wu

  3. 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 2007 Pittsburgh Workshop Canglin Wu

  4. 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 DEDiscoverDifferential Equation Modeling Solution 2007 Pittsburgh Workshop Canglin Wu

  5. DEDiscoverDifferential Equation Modeling Solution Model input and solver selection 2007 Pittsburgh Workshop Canglin Wu

  6. DEDiscoverDifferential Equation Modeling olution Parameters and initial conditions 2007 Pittsburgh Workshop Canglin Wu

  7. Simulation Support Several ODE and DDE solvers Real-time solutions allow interactive exploration Tabular and Graphical display of results Customizable displays DEDiscoverDifferential Equation Modeling Solution 2007 Pittsburgh Workshop Canglin Wu

  8. DEDiscoverDifferential Equation Modeling Solution Simulation result - Combined plot 2007 Pittsburgh Workshop Canglin Wu

  9. DEDiscoverDifferential Equation Modeling Solution Simulation result - Individual plot 2007 Pittsburgh Workshop Canglin Wu

  10. DEDiscoverDifferential Equation Modeling Solution Simulation result - Table 2007 Pittsburgh Workshop Canglin Wu

  11. 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 2007 Pittsburgh Workshop Canglin Wu

  12. 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 2007 Pittsburgh Workshop Canglin Wu

  13. DEDiscoverDifferential Equation Modeling Solution Formula Syntax • Indicator function I(tau_T,100)(t) tau_T<I<100 I[tau_T,100)(t) tau_T<=I<100 I(tau_T,100](t) tau_T<I<=100 I[tau_T,100](t) tau_T<=I<=100 • Initial condition in formula, D(0) • Comment, // for comment one line, /* */ for comment multiple lines 2007 Pittsburgh Workshop Canglin Wu

  14. 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 2007 Pittsburgh Workshop Canglin Wu

  15. 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 2007 Pittsburgh Workshop Canglin Wu

  16. DEDiscoverDifferential Equation Modeling Solution Operator • + Add • - Subtract • * Multiply • / Divide • % Modulus • ^ Power: y = x ^ 2( ) • () Parenthesis. For example: (2 + 3) * 5 2007 Pittsburgh Workshop Canglin Wu

  17. 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 2007 Pittsburgh Workshop Canglin Wu

  18. 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 2007 Pittsburgh Workshop Canglin Wu

  19. DEDiscoverDifferential Equation Modeling Solution Download • Log in CBIM website first • Download at http://cbim.urmc.rochester.edu/software • Install DEDiscover package in your computer 2007 Pittsburgh Workshop Canglin Wu

  20. DEDiscoverDifferential Equation Modeling Solution DEDicover DEMO 2007 Pittsburgh Workshop Canglin Wu

  21. DEDiscoverDifferential Equation Modeling Solution Acknowledgment • NIAID/NIH grant NO1 AI50020 Center 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 2007 Pittsburgh Workshop Canglin Wu

  22. DEDiscoverDifferential Equation Modeling Solution Thanks Q & A 2007 Pittsburgh Workshop Canglin Wu

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