更改

<math>\Delta \Gamma_{\alpha}(\epsilon) =  \frac{\sum_{i = 1}^{r} \sigma_{i}^{\alpha}}{r} -  \frac{\sum_{i = 1}^{N} \sigma_{i}^{\alpha}}{N} </math>

<math>\Delta \Gamma_{\alpha}(\epsilon) =  \frac{\sum_{i = 1}^{r} \sigma_{i}^{\alpha}}{r} -  \frac{\sum_{i = 1}^{N} \sigma_{i}^{\alpha}}{N} </math>

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 is 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=====