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In summary, the advantage of this method for quantifying causal emergence is that it can quantify causal emergence more objectively without relying on a specific coarse-graining strategy. The disadvantage of this method is that to calculate [math]\Gamma_{\alpha}[/math], it is necessary to perform [[SVD decomposition]] on <math>P</math> in advance. As a result, the computational complexity is [math]O(N^3)[/math], which is higher than the computational complexity of <math>EI</math>. Moreover, [math]\Gamma_{\alpha}[/math> cannot be explicitly decomposed into two components: determinism and degeneracy.

In summary, the advantage of this method for quantifying causal emergence is that it can quantify causal emergence more objectively without relying on a specific coarse-graining strategy. The disadvantage of this method is that to calculate [math]\Gamma_{\alpha}[/math], it is necessary to perform [[SVD decomposition]] on <math>P</math> in advance. As a result, the computational complexity is [math]O(N^3)[/math], which is higher than the computational complexity of <math>EI</math>. Moreover, [math]\Gamma_{\alpha}[/math] cannot be explicitly decomposed into two components: determinism and degeneracy.

 

=====Specific Example=====

=====Specific Example=====