7:39 AM
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Hartshorne writes that a curve is a finite integral separate one-dimensional scheme on field k. I think that a curve is a "one-dimensional algebraic variety" here. Let the set of the entire "one-dimensional algebraic variety" be A , and the set of the entire scheme be B, is it true that A⊂B? Is i...

11 hours later…
6:29 PM
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The interaction information (II) in 3D is defined as a generalization of the 2D mutual information (MI). $$\begin{eqnarray} I(X:Y:Z) &=& I(X:Y) - I(X:Y|Z) \\ &=& H(X) + H(Y)+H(Z) - H(XY) - H(XZ) - H(YZ) + H(XYZ) \end{eqnarray}$$ II can be negative, for example for $Z = \mathrm{XOR}(X, Y)$. It i...

In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intimately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable. Not limited to real-valued...

7:05 PM
BTW the same tag was created at least twice in the past: March 2020 and June 2020.
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