A tool to approximate viability kernels capture basins and resilience values
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A tool to approximate viability kernels, capture basins and resilience values. Kernel Approximation for VIAbility and Resilience. Written in Java programming language Regular grid / active learning algorithm Capture basins and resilience values are computed in dim d

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Kernel approximation for viability and resilience
Kernel Approximation for VIAbility and Resilience resilience values

  • Written in Java programming language

    • Regular grid / active learning algorithm

    • Capture basins and resilience values are computed in dim d

    • Heavy or optimal controllers

    • Two modes: GUI and batch mode

  • http://trac.clermont.cemagref.fr/projets/Kaviar/wiki/download#Download


Installation and running
Installation and running resilience values

http://trac.clermont.cemagref.fr/projets/Kaviar/wiki/download#Download

  • Requires the java virtual machine (Sun’s JRE environment 5 or later compulsory)

  • 2 set up

    • .jar file to test the models already implemented

    • .zip file to implement new models


Gui mode
GUI mode resilience values

  • Display window

  • Console window


Gui mode cont
GUI mode (cont) resilience values

Dynamical system settings

Control bounds

Time step

Function of the size of the grid

Study of the dynamics!!!

Viability constraint set


Gui mode cont1
GUI mode (cont) resilience values

Viability controller config

General settings

Optimization settings

Algorithm type

Visualize the individual trajectories

- Simple: gradient descent from the minimal values of the controls

- Double: min and max values

- Conjugate gradient

- Double conjugate gradient

- Newton method


Gui mode cont2
GUI mode (cont) resilience values

SVM configuration

Stopping criterion of the SVMs computation algorithm

SVM algorithm

Bandwidth

  • big C : hard margin(no misclassification)

  • small C: soft margin

Only the gaussian kernel is implemented

Control the “smoothness” of the SVM function

- Small gamma: smooth

- Big gamma: less smooth

- C-SMO: see libSVM

- Simple SVM

- Balk: automative bandwidth tuning

- Soft-Balk: balk with soft margin


Gui mode cont3
GUI mode (cont) resilience values

Execution and control


Gui mode cont4
GUI mode (cont) resilience values

Indicators + logs


Example on the population problem
Example on the population problem resilience values

  • Viability kernel approximation

    • Play with dt, # time steps, # points (and show trajectories)

      • To obtain a “good” approximation, the dt value must be chosen accordingly the number of points and time steps

      • Inner approximation sometimes…

    • Save the results and reload them


Example on the population problem1
Example on the population problem resilience values

  • Controller – Kernel approx with dt = 0.05, 6 time steps, 31 points

    • A point out of the viability kernel approximation

      • x0 = 2, y0 = 0.8, 20 time steps, 3 time steps anticipation, 3 distance SVM, dist(K) = 0.025

    • Inside the viability kernel

      • x0 = 2, y0 = 0.5, 150 time steps

    • More time steps anticipation: 15

    • Bigger SVM value: 30

    • Same parameters, with 1 time step for the viability kernel approximation


Adding a dynamical system
Adding a dynamical system resilience values

  • Creation of a new class file (for instance MyClass.java)

    • Extend Dynamic_System if viability kernel approximation

    • Extend Dynamic_System_Target if capture basins approximation

    • Extend Dynamic_System_Resilience if resilience values

  • In this class, create a main method to add your model and launch the software

    Public static void main (String[]args){

    //init

    Kaviar kaviar = new Kaviar();

    //Optional: to add default models

    Kaviar.addModels(Kaviar.DEFAULT_MODEL);

    //Optional: to add one of the default models

    //Kaviar.addModels(Population.class);

    //replace my model by the name of your model

    Kaviar.addModels(MyModel.class);

    //Launch the GUI

    Kaviar.startGUI();

    }


Myclass java extends dynamical system
MyClass.java resilience values(extends Dynamical_System)


Myclass java extends dynamical system target
MyClass.java resilience values(extends Dynamical_System_Target)

Previous+


Myclass java extends dynamical system resilience
MyClass.java resilience values(extends Dynamical_System_Resilience)

Previous+


Example on the abrams strogatz model
Example on the Abrams&Strogatz model resilience values

  • Dynamics and constraints

    • 2 languages A and B in competition, no bilingual people

      • σA: density of speakers of language A (in % - [0;1]).

      • Parameter a: volatility of language A (a > 1 leads a scenario of dominance of 1 language)

      • Parameter s: prestige of language A (s = 0.5: the two languages are socially equivalent – [0;1])

    • Government, institution etc. can play on the prestige of one language, but modifications take time

    • We consider that one language is endangered when its proportion of speakers is less that 20%

    • with


Example on the abrams strogatz model1
Example on the Abrams&Strogatz model resilience values

  • Resilience values

    • Endangered language doesn’t mean that the language is dead. Is there any action policies that allows the system to recover?

    • At which cost?

      • λ = 1: measure the time the system is deprived from its property of interest

      • λ = c1*time + c2(distance(σA from viability))


Example on the abrams strogatz model2
Example on the Abrams&Strogatz model resilience values

  • Optimal control

    • Compute the resilience values with the following parameters:

      • dt =0.2, dc = 0.5, double optimization, C0 = 1, C1 = 300, 31 points, 6 time steps, inner approx

      • a = 2: dominance of one language

      • a = 0.2: stable coexistence

    • Control of the system:

      • x0 =0.95, y0= 0.95 and x0 =0.7, y0= 0.95

      • Optimal control outside the viability kernel

      • Heavy control once the system is back to the kernel


Batch mode
Batch mode resilience values

  • .simu files are needed

    • Create them following a given template

    • Use the GUI interface

  • java -cp Kaviar-1.1.jar Appli/Batch Conso.simu

  • 2 files: .svm + .log files, in the Conso… directory


  • Batch mode1
    Batch mode resilience values

    • java -cp Kaviar-1.1.jar Appli/Batch Conso.simu -v

    • 9*2 files: .svm + .log files, in the Conso… directory


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