3 problems

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Conjecture that a flattened-noise channel is at least as informative for every Boolean function
Flattened-noise informativeness conjecture. For every such $b$ ,
Conjectureopenboolean-functions information-theory principal-inertia-componentsarXiv posted 3 days ago
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Conjecture on equal principal inertia components maximizing binary mutual information
Equal-PIC maximization conjecture. The mutual information $I(b(X);Y)$ is maximized when every principal inertia component equals the largest principal inertia component.
Conjectureopeninformation-theory principal-inertia-componentsarXiv posted 3 days ago
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The equal-principal-inertia-components conjecture for mutual information
Let $X$ and $Y$ be random variables, let $f(X)$ be a one-bit function of $X$ , and let the principal inertia components of the joint distribution of $X$ and $Y$ be given. Equal-prin…
Conjectureopeninformation-theory principal-inertia-componentsarXiv posted 3 days ago

Conjecture that a flattened-noise channel is at least as informative for every Boolean function