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ReactionNetworks :: negativeWeightedLaplacian

negativeWeightedLaplacian -- Computes the negative of the weighted Laplacian matrix of a Reaction Network.

Synopsis

Description

Computes the negative of the weighted Laplacian matrix of a Reaction Network.

i1 : N = reactionNetwork "A <--> B"

o1 = A-->B
     B-->A

o1 : ReactionNetwork
i2 : L = negativeWeightedLaplacian N

o2 = | -kk_{0, 1} kk_{0, 1}  |
     | kk_{1, 0}  -kk_{1, 0} |

                                                        2                                                  2
o2 : Matrix (QQ[xx , xx , cc , cc , kk      , kk      ])  <--- (QQ[xx , xx , cc , cc , kk      , kk      ])
                  A    B    A    B    {0, 1}    {1, 0}               A    B    A    B    {0, 1}    {1, 0}

A bigger example:

i3 : N = oneSiteModificationA()

o3 = S_0+E-->X
     X-->S_0+E
     X-->E+S_1
     S_1+F-->Y
     Y-->S_1+F
     Y-->S_0+F

o3 : ReactionNetwork
i4 : L = negativeWeightedLaplacian N

o4 = | -kk_{0, 1} kk_{0, 1}            0         0          0                
     | kk_{1, 0}  -kk_{1, 0}-kk_{1, 2} kk_{1, 2} 0          0                
     | 0          0                    0         0          0                
     | 0          0                    0         -kk_{3, 4} kk_{3, 4}        
     | 0          0                    0         kk_{4, 3}  -kk_{4, 3}-kk_{4,
     | 0          0                    0         0          0                
     ------------------------------------------------------------------------
        0         |
        0         |
        0         |
        0         |
     5} kk_{4, 5} |
        0         |

                                                                                                                                                6                                                                                                                                          6
o4 : Matrix (QQ[xx   , xx , xx , xx   , xx , xx , cc   , cc , cc , cc   , cc , cc , kk      , kk      , kk      , kk      , kk      , kk      ])  <--- (QQ[xx   , xx , xx , xx   , xx , xx , cc   , cc , cc , cc   , cc , cc , kk      , kk      , kk      , kk      , kk      , kk      ])
                  S_0    E    X    S_1    F    Y    S_0    E    X    S_1    F    Y    {0, 1}    {1, 0}    {1, 2}    {3, 4}    {4, 3}    {4, 5}               S_0    E    X    S_1    F    Y    S_0    E    X    S_1    F    Y    {0, 1}    {1, 0}    {1, 2}    {3, 4}    {4, 3}    {4, 5}

See also

Ways to use negativeWeightedLaplacian :

For the programmer

The object negativeWeightedLaplacian is a method function.