**********************************************************************************
*                                                                                                      
* GENERATING SERIES approach for Structural Identifiability Analysis   
*                                                                                                      
* Oana Chis, Julio R. Banga and Eva Balsa-Canto                                
*  BioProcess Engineering Group, IIM-CSIC, Vigo-Spain                        
*  contact: [chisoana,julio,ebalsa]@iim.csic.es                                     
*                                                                                                        
**********************************************************************************

Matlab version=7.6.0.324 (R2008a)
Computer=PCWIN
options:
                verbose: 1
                 noRank: 0
    problem_folder_path: 'C:\data\Tom\Research\Raedler\mRNA-Helmholtz\Tom\GenSSI\Results\Arabidopsis\run4'

STRUCTURAL IDENTIFIABILITY ANALYSIS FOR: Arabidopsis Model
 

***************
* INPUT DATA 
***************

-----> Maximum number of derivatives for the analysis: 5
-----> Dynamic model:
	A1=p1*x6/(p3+x6)-p5*x1/(p12+x1)
 
	A2=p19*x1-p22*x2+p23*x3-p6*x2/(p13+x2)
 
	A3=p22*x2-p23*x3-p7*x3/(p14+x3)
 
	A4=p2*p4^2/(p4^2+x3^2)-p8*x4/(p15+x4)
 
	A5=p20*x4-p24*x5+p25*x6-p9*x5/(p16+x5)
 
	A6=p24*x5-p25*x6-p10*x6/(p17+x6)
 
	A7=p21-p11*x7/(p18+x7)
 
-----> Control variables:
	G1=[      p26*x7,           0,           0,           0,           0,           0, -p21-p27*x7]
 
-----> Observables:
	H1=x1
 
	H2=x4
 
-----> Initial conditions:
	[ 0, 0, 0, 0, 0, 0, 0]
 
-----> Parameters to be considered in the analysis:
	[  p1,  p2,  p5,  p8, p10, p11, p12, p15, p18, p27, p26]
 



Report inputs elapsed time: 0.0054866
*******************************
-> COMPUTE LIE DERIVATIVES
*******************************

COMPUTING LIE DERIVATIVES OF ORDER 1
.................................................................
   ->The rank of the Jacobian generated by 1 derivatives is  1.
   ->The rank of the next Jacobian is expected to be maximum 2.
.................................................................
  
COMPUTING LIE DERIVATIVES OF ORDER 2
.................................................................
   ->The rank of the Jacobian generated by 2 derivatives is  3.
   ->The rank of the next Jacobian is expected to be maximum 5.
.................................................................
  
COMPUTING LIE DERIVATIVES OF ORDER 3
.................................................................
   ->The rank of the Jacobian generated by 3 derivatives is  7.
   ->The rank of the next Jacobian is expected to be maximum 11.
.................................................................
  
COMPUTING LIE DERIVATIVES OF ORDER 4
.................................................................
   ->The rank of the Jacobian generated by 4 derivatives is  9.
   ->The rank of the next Jacobian is expected to be maximum 11.
.................................................................
  
COMPUTING LIE DERIVATIVES OF ORDER 5
.................................................................
   ->The rank of the Jacobian generated by 5 derivatives is 11.
Compute Lie derivatives elapsed time: 9.0393


***************************************
-> COMPUTE IDENTIFIABILITY TABLEAU
***************************************

 ----->The rank of the full Jacobian matrix is 11 

 ---->THE RANK OF THE FULL JACOBIAN IS COMPLETE, THUS AT LEAST LOCAL IDENTIFIABILITY IS GUARANTEED.
Compute tableau elapsed time: 0.23786


************************************************
-> COMPUTE REDUCED IDENTIFIABILITY TABLEAUS
************************************************


*****************************************************
-> THE RELATIONS NEEDED FOR COMPUTING THE PARAMETERS
*****************************************************

                                                                                                 p2-c1
                                                                                         -p2*p8/p15-c2
                                                                                            p21*p26-c3
                                                                      p2*(p8^2/p15^2+2*p2*p8/p15^2)-c4
                                                                                   -p21*p11/p18*p26-c5
                                                                                    -p21*p26*p5/p12-c6
                                                                                       -p21*p27*p26-c7
                                                                                   p2*p20*p24*p1/p3-c8
                                                          p21*(p11^2/p18^2*p26+2*p21*p11/p18^2*p26)-c9
 p2*(-p8/p15*p20*p24*p1/p3+p20*((-p24-p9/p16)*p24*p1/p3+p24*(-p1/p3*p5/p12+(-p25-p10/p17)*p1/p3)))-c10
                                                p21*(-p27*p11/p18*p26*p5/p12+4*p26^2*p21*p5/p12^2)-c11
 
Compute reduced tableau  elapsed time: 1.432


******************************************************************************************
-> DETECT (DIRECT) STRUCTURALLY GLOBALLY IDENTIFIABLE PARAMETERS AND REORGANIZES TABLEAU
*******************************************************************************************



 -> STRUCTURALLY GLOBALLY IDENTIFIABLE PARAMETERS DETERMINED DIRECTLY 
   (parameters corresponding to one non-zero element in the reduced identifiability tableau)

----->The parameter p2 is structurally globally identifiable. It has the solution:
       p2= c1.
----->The parameter p26 is structurally globally identifiable. It has the solution:
       p26= c3/p21.
----->The parameter p27 is structurally globally identifiable. It has the solution:
       p27= -c7/p21/p26.
----->The parameter p1 is structurally globally identifiable. It has the solution:
       p1= c8/p2/p20/p24*p3.


************************************************************************************************************
->THE REMAINING PARAMETERS (APART FROM IDENTIFIABLE OR NON-IDENTIFIABLE), AND THE CORRESPONDING RELATIONS  
************************************************************************************************************

-----> Parameters: 
[  p5,  p8, p10, p11, p12, p15, p18]
 
-----> Relations: 
                                                                                         -p2*p8/p15-c2
                                                                      p2*(p8^2/p15^2+2*p2*p8/p15^2)-c4
                                                                                   -p21*p11/p18*p26-c5
                                                                                    -p21*p26*p5/p12-c6
                                                          p21*(p11^2/p18^2*p26+2*p21*p11/p18^2*p26)-c9
 p2*(-p8/p15*p20*p24*p1/p3+p20*((-p24-p9/p16)*p24*p1/p3+p24*(-p1/p3*p5/p12+(-p25-p10/p17)*p1/p3)))-c10
                                                p21*(-p27*p11/p18*p26*p5/p12+4*p26^2*p21*p5/p12^2)-c11
 
**********************************************************************************
-> COMPUTE HIGHER ORDER REDUCED IDENTIFIABILITY TABLEAU(S) 

   (display the group of 2/more depending parameters,
            the associated algebraic relations,  
            the corresponding solution (solutions))

**********************************************************************************

-----> The group of parameters to be considered in the calculus and the corresponding relations:

-> Parameters: 
   	[p8	p15	]


-> Relations: 
                    -p2*p8/p15-c2
 p2*(p8^2/p15^2+2*p2*p8/p15^2)-c4
 
-----> THE SYMBOLIC SOLUTION OF THE REMAINING PARAMETERS: 
-----> The parameter p8 has the solution/solutions: 
  2*p2^2*c2/(c2^2-c4*p2)
-----> The parameter p15 has the solution/solutions: 
  -2*p2*c2^2/(c2^2-c4*p2)
....................................................................................................

-----> The group of parameters to be considered in the calculus and the corresponding relations:

-> Parameters: 
   	[p11	p18	]


-> Relations: 
                          -p21*p11/p18*p26-c5
 p21*(p11^2/p18^2*p26+2*p21*p11/p18^2*p26)-c9
 
-----> THE SYMBOLIC SOLUTION OF THE REMAINING PARAMETERS: 
-----> The parameter p11 has the solution/solutions: 
  2*p21*c5^2/(-c5^2+c9*p21*p26)
-----> The parameter p18 has the solution/solutions: 
  -2*p21^2*c5/(-c5^2+c9*p21*p26)*p26
....................................................................................................

-----> The remaining group of parameters, relations and the corresponding solutions:

-> Parameters: 
   	[p5	p10	p12	]


-> Relations: 
                                                                                    -p21*p26*p5/p12-c6
 p2*(-p8/p15*p20*p24*p1/p3+p20*((-p24-p9/p16)*p24*p1/p3+p24*(-p1/p3*p5/p12+(-p25-p10/p17)*p1/p3)))-c10
                                                p21*(-p27*p11/p18*p26*p5/p12+4*p26^2*p21*p5/p12^2)-c11
 
**********************************************************************************
-> THE REDUCED TABLEAUS OF THE REDUCED TABLEAU  

   (for the remaining set of parameters and relations)  
**********************************************************************************

-----> The group of parameters to be considered in the calculus and the corresponding relations:

-> Parameters: 
   	[p5	p12	]


-> Relations: 
                                     -p21*p26*p5/p12-c6
 p21*(-p27*p11/p18*p26*p5/p12+4*p26^2*p21*p5/p12^2)-c11
 
-----> THE SYMBOLIC SOLUTION OF THE REMAINING PARAMETERS: 
-----> The parameter p5 has the solution/solutions: 
  4*p21*p26*p18*c6/(p11*p27*c6-c11*p18)
-----> The parameter p12 has the solution/solutions: 
  -4*p18*c6^2/(p11*p27*c6-c11*p18)
....................................................................................................

-----> The remaining group of parameters, relations and the corresponding solutions:

-> Parameters: 
   	[p10	]


-> Relations: 
p2*(-p8/p15*p20*p24*p1/p3+p20*((-p24-p9/p16)*p24*p1/p3+p24*(-p1/p3*p5/p12+(-p25-p10/p17)*p1/p3)))-c10
 
-----> THE SYMBOLIC SOLUTION OF THE REMAINING PARAMETERS: 
-----> The parameter p10 has the solution/solutions: 
  -(p2*p20*p24*p1*p8*p16*p12+p2*p20*p24^2*p1*p15*p12*p16+p2*p20*p24*p1*p15*p12*p9+p2*p20*p24*p1*p15*p16*p5+p2*p20*p24*p1*p15*p16*p25*p12+c10*p15*p3*p16*p12)/p15/p16/p12/p2/p20/p24*p17/p1
Order tableau elapsed time: 1.2582


***************************************************************

 -----> THE MODEL IS STRUCTURALLY GLOBALLY IDENTIFIABLE 

***************************************************************

        The structurally globally identifiable parameters are: 

     	[      p2	      p26	      p27	      p1	      p8	      p15	      p11	      p18	      p5	      p12	      p10	]


Report results elapsed time: 0.0010475
Total elapsed time: 11.9791
