heatkernel

Parameters

time:

Value for the time parameter desired in case of polynomial matrix. Is mandatory in such case.

lambda:

Value of the parameter for the Heat Kernel method, look the bibliography. This parameter is mandatory.

D:

Matrix of direct influences. This value is mandatory.

f:

Name of the variable to store the indirect influences vector.

d:

Name of the variable to store the indirect dependences vector.

T:

Name of the variable to store the indirect influences matrix.

Description

This function gives the vector of indirect influences and dependences and the matrix of indirect influences of a given matrix of direct influences according with the Heat Kernel method. If the matrix of direct influences has polynomial entries the function needs the time parameter. For more info look the bibliography.

Examples

D = [1 0 1;0 0 0;0 0 6] // Define the matrix of direct influences. [T,d,f] = heatkernel(D,1) // Returns the matrix of indirect influences T, the vector of indirect dependences d and the vector of indirect influences f. bar(d) bar(f) D = sparse([1,2;2,3;3,1;4,1],[1,2,4,1],[4,4]) // Define a sparse matrix [T,d,f] = heatkernel(D,1) t = poly(0,'t') // Define the variable t. D = [t 1-t;t^2 1] // Define a 2x2 matrix with polynomial entries. [T,d,f] = heatkernel(D,1,0) // Apply the Heat Kernel method to the matrix D with time 0. bar(d) bar(f) [T,d,f] = heatkernel(D,1,1) // Apply the Heat Kernel method to the matrix D with time 1. bar(d) bar(f)

See also

• micmac
• pagerank
• pwp_method
• pwp_method_inv
• heatkernel_inv

Authors

• Jorge Catumba

Bibliography

F. Chung, The heat kernel as the pagerank of a graph, Proc. Natl. Acad. Sci. 104 (50) 19735-19740.

R. Díaz, Indirect Influences, Advanced Studies in Contemporary Mathematics 23 (2013) 29-41.