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Theoretical Model

An adapted Markov-Chain Model is used to predict the possible probability distributions. 

 
-3->DISTANCE=2,[GRID02]=testgrid(DISTANCE)
 DISTANCE  =
 
    2.  
 GRID02  =
 
!.  .  .  .  .  !
!               !
!.  .  .  .  .  !
!               !
!.  .  F  .  .  !
!               !
!.  .  .  .  .  !
!               !
!.  .  .  .  .  !
 
-3->[W02]=transprob(GRID02)
 W02  =
 
 
         column  1 to 17
 
    0.6666667    0.1111111    0.           0.           0.           0.1111111    0.1111111    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.         
    0.1111111    0.4444444    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.1111111    0.4444444    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.1111111    0.4444444    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.1111111    0.6666667    0.           0.           0.           0.1111111    0.1111111    0.           0.           0.           0.           0.           0.           0.         
    0.1111111    0.1111111    0.           0.           0.           0.4444444    0.1111111    0.           0.           0.           0.1111111    0.1111111    0.           0.           0.           0.           0.         
    0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.           0.         
    0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.         
    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.         
    0.           0.           0.           0.1111111    0.1111111    0.           0.           0.           0.1111111    0.4444444    0.           0.           0.           0.1111111    0.1111111    0.           0.         
    0.           0.           0.           0.           0.           0.1111111    0.1111111    0.           0.           0.           0.4444444    0.1111111    0.           0.           0.           0.1111111    0.1111111  
    0.           0.           0.           0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111  
    0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111  
    0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.           0.           0.           0.1111111    0.4444444    0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.           0.           0.           0.4444444    0.1111111  
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111  
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111  
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.1111111    0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111  
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111  
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111  
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.         
 
         column 18 to 25
 
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.1111111    0.           0.           0.           0.           0.           0.           0.         
    0.1111111    0.1111111    0.           0.           0.           0.           0.           0.         
    0.1111111    0.1111111    0.1111111    0.           0.           0.           0.           0.         
    0.           0.1111111    0.1111111    0.           0.           0.           0.           0.         
    0.           0.           0.           0.1111111    0.1111111    0.           0.           0.         
    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.         
    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.         
    0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111  
    0.           0.1111111    0.4444444    0.           0.           0.           0.1111111    0.1111111  
    0.           0.           0.           0.6666667    0.1111111    0.           0.           0.         
    0.1111111    0.           0.           0.1111111    0.4444444    0.1111111    0.           0.         
    0.1111111    0.1111111    0.           0.           0.1111111    0.4444444    0.1111111    0.         
    0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.4444444    0.1111111  
    0.           0.1111111    0.1111111    0.           0.           0.           0.1111111    0.6666667  
 
-3->W022=W02'
 W022  =
 
 
         column  1 to 17
 
    0.6666667    0.1111111    0.           0.           0.           0.1111111    0.1111111    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.         
    0.1111111    0.4444444    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.1111111    0.4444444    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.1111111    0.4444444    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.1111111    0.6666667    0.           0.           0.           0.1111111    0.1111111    0.           0.           0.           0.           0.           0.           0.         
    0.1111111    0.1111111    0.           0.           0.           0.4444444    0.1111111    0.           0.           0.           0.1111111    0.1111111    0.           0.           0.           0.           0.         
    0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.           0.         
    0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.         
    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.         
    0.           0.           0.           0.1111111    0.1111111    0.           0.           0.           0.1111111    0.4444444    0.           0.           0.           0.1111111    0.1111111    0.           0.         
    0.           0.           0.           0.           0.           0.1111111    0.1111111    0.           0.           0.           0.4444444    0.1111111    0.           0.           0.           0.1111111    0.1111111  
    0.           0.           0.           0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111  
    0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111  
    0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.           0.           0.           0.1111111    0.4444444    0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.           0.           0.           0.4444444    0.1111111  
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111  
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.1111111    0.           0.           0.1111111  
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.1111111    0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111    0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111  
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111    0.1111111  
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.1111111  
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.           0.         
 
         column 18 to 25
 
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.           0.           0.           0.           0.           0.           0.           0.         
    0.1111111    0.           0.           0.           0.           0.           0.           0.         
    0.1111111    0.1111111    0.           0.           0.           0.           0.           0.         
    0.1111111    0.1111111    0.1111111    0.           0.           0.           0.           0.         
    0.           0.1111111    0.1111111    0.           0.           0.           0.           0.         
    0.           0.           0.           0.1111111    0.1111111    0.           0.           0.         
    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.           0.         
    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111    0.         
    0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.1111111    0.1111111  
    0.           0.1111111    0.4444444    0.           0.           0.           0.1111111    0.1111111  
    0.           0.           0.           0.6666667    0.1111111    0.           0.           0.         
    0.1111111    0.           0.           0.1111111    0.4444444    0.1111111    0.           0.         
    0.1111111    0.1111111    0.           0.           0.1111111    0.4444444    0.1111111    0.         
    0.1111111    0.1111111    0.1111111    0.           0.           0.1111111    0.4444444    0.1111111  
    0.           0.1111111    0.1111111    0.           0.           0.           0.1111111    0.6666667  
 

 
-3->INPUT2=[1 0 0 0 0; 0 0 0 0 0; 0 0 0 0 0; 0 0 0 0 0; 0 0 0 0 0]
 INPUT2  =
 
    1.    0.    0.    0.    0.  
    0.    0.    0.    0.    0.  
    0.    0.    0.    0.    0.  
    0.    0.    0.    0.    0.  
    0.    0.    0.    0.    0.  

 
-3->SHOW=0,RUNS=50,[OUTPUT]=fieldprob(W022,INPUT,RUNS, SHOW)

 OUTPUT  =
 
 
         column  1 to 18
 
    0.0405487    0.0404026    0.0402253    0.0400678    0.0399905    0.0404026    0.0402975    0.0401410    0.0399969    0.0399218    0.0402253    0.0401410    0.04    0.0398590    0.0397747    0.0400678    0.0399969    0.0398590  
 
         column 19 to 25
 
    0.0397087    0.0396079    0.0399905    0.0399218    0.0397747    0.0396079    0.0394703  

 
-3->SHOW=0,RUNS=60,[OUTPUT]=fieldprob(W022,INPUT,RUNS, SHOW)

 OUTPUT  =
 
 
         column  1 to 18
 
    0.0401716    0.0401262    0.0400711    0.0400223    0.0399986    0.0401262    0.0400934    0.0400445    0.0399995    0.0399762    0.0400711    0.0400445    0.04    0.0399555    0.0399289    0.0400223    0.0399995    0.0399555  
 
         column 19 to 25
 
    0.0399075    0.0398753    0.0399986    0.0399762    0.0399289    0.0398753    0.0398312  
 
-3->st_deviation(OUTPUT)
 ans  =
 
    0.0000838  
 
-3->SHOW=0,RUNS=55,[OUTPUT]=fieldprob(W022,INPUT,RUNS, SHOW)

 OUTPUT  =
 
 
         column  1 to 18
 
    0.0403066    0.0402252    0.0401266    0.0400390    0.0399964    0.0402252    0.0401666    0.0400792    0.0399988    0.0399570    0.0401266    0.0400792    0.04    0.0399208    0.0398734    0.0400390    0.0399988    0.0399208  
 
         column 19 to 25
 
    0.0398358    0.0397787    0.0399964    0.0399570    0.0398734    0.0397787    0.0397007  
 
 
-->run55=[ 0.0403066    0.0402252    0.0401266    0.0400390    0.0399964    0.0402252    0.0401666    0.0400792    0.0399988    0.0399570 0.0401266    0.0400792    0.04    0.0399208    0.0398734    0.0400390    0.0399988    0.0399208   0.0398358    0.0397787    0.0399964    0.0399570    0.0398734    0.0397787    0.0397007 ]
 run55  =
 
 
         column  1 to 11
 
    0.0403066    0.0402252    0.0401266    0.040039    0.0399964    0.0402252    0.0401666    0.0400792    0.0399988    0.039957    0.0401266  
 
         column 12 to 23
 
    0.0400792    0.04    0.0399208    0.0398734    0.040039    0.0399988    0.0399208    0.0398358    0.0397787    0.0399964    0.039957    0.0398734  
 
         column 24 to 25
 
    0.0397787    0.0397007  
 
-->st_deviation(run55)
 ans  =
 
    0.0001491  
 
-->run60=[0.0401716    0.0401262    0.0400711    0.0400223    0.0399986    0.0401262    0.0400934    0.0400445    0.0399995    0.0399762    0.0400711    0.0400445    0.04    0.0399555    0.0399289    0.0400223    0.0399995    0.0399555 0.0399075    0.0398753    0.0399986    0.0399762    0.0399289    0.0398753    0.0398312]
 run60  =
 
 
         column  1 to 11
 
    0.0401716    0.0401262    0.0400711    0.0400223    0.0399986    0.0401262    0.0400934    0.0400445    0.0399995    0.0399762    0.0400711  
 
         column 12 to 23
 
    0.0400445    0.04    0.0399555    0.0399289    0.0400223    0.0399995    0.0399555    0.0399075    0.0398753    0.0399986    0.0399762    0.0399289  
 
         column 24 to 25
 
    0.0398753    0.0398312  
 
-->st_deviation(run60)
 ans  =
 
    0.0000838  
 
-->run50=[0.0405487    0.0404026    0.0402253    0.0400678    0.0399905    0.0404026    0.0402975    0.0401410    0.0399969    0.0399218    0.0402253    0.0401410    0.04    0.0398590    0.0397747    0.0400678    0.0399969    0.0398590 0.0397087    0.0396079    0.0399905    0.0399218    0.0397747    0.0396079    0.0394703  ]
 run50  =
 
 
         column  1 to 11
 
    0.0405487    0.0404026    0.0402253    0.0400678    0.0399905    0.0404026    0.0402975    0.040141    0.0399969    0.0399218    0.0402253  
 
         column 12 to 23
 
    0.040141    0.04    0.039859    0.0397747    0.0400678    0.0399969    0.039859    0.0397087    0.0396079    0.0399905    0.0399218    0.0397747  
 
         column 24 to 25
 
    0.0396079    0.0394703  
 
-->st_deviation(run50)
 ans  =
 
    0.0002654  
-->0.04*55
 ans  =
 
    2.2


Gerd Doeben-Henisch 2012-03-31