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A Counterexample to the Chain Rule for Conditional HILL Entropy
Computational Entropy HILL Entropy Chain Rule
2016/1/7
Most entropy notions H(.) like Shannon or min-entropy satisfy a chain rule
stating that for random variables X, Z and A we have H(X|Z, A) ≥ H(X|Z) −
|A|. That is, by conditioning on A the entr...
Computational notions of entropy (a.k.a. pseudoentropy) have
found many applications, including leakage-resilient cryptography, deterministic
encryption or memory delegation. The most important tool...
A chain rule formula in BV and applications to conservation laws
chain rule formula BV conservation laws
2010/11/9
In this paper we prove a new chain rule formula for the distributional derivative of the composite function $v(x)=B(x,u(x))$, where $u:]a,b[\to\R^d$ has bounded variation, $B(x,\cdot)$ is continuousl...
A GENERALIZED CHAIN RULE FOR FORMAL POWER SERIES
Formal power series composition chain rule right distributive law
2008/11/25
Given a formal power series g(x) = P1n=0 bn xn and a nonunit f(x) = P1 n=1 an xn,
it is well-known that the derivative of the composition of formal power series satisfies the
Chain Rule, that is, (g...