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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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

A tool to approximate viability kernels, capture basins and resilience values


Kernel approximation for viability and resilience

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

    • 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

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

  • Display window

  • Console window


Gui mode cont

GUI mode (cont)

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)

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)

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)

Execution and control


Gui mode cont4

GUI mode (cont)

Indicators + logs


Example on the population problem

Example on the population problem

  • 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

  • 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

  • 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 (extends Dynamical_System)


Myclass java extends dynamical system target

MyClass.java (extends Dynamical_System_Target)

Previous+


Myclass java extends dynamical system resilience

MyClass.java (extends Dynamical_System_Resilience)

Previous+


Example on the abrams strogatz model

Example on the Abrams&Strogatz model

  • 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

    • 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

  • 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

  • .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

    • 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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