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 Mar31 accepted Example of $H^n(X,R)$ not equal to $Hom(H_n(X,R),R)$ Mar31 comment Example of $H^n(X,R)$ not equal to $Hom(H_n(X,R),R)$ Yes, thanks! It's exactly what I wanted to know. Mar31 revised Example of $H^n(X,R)$ not equal to $Hom(H_n(X,R),R)$ edited body Mar31 comment Example of $H^n(X,R)$ not equal to $Hom(H_n(X,R),R)$ Thanks a lot for the answer. I had made a mistake in the question...could you please update? Mar31 revised Example of $H^n(X,R)$ not equal to $Hom(H_n(X,R),R)$ added 118 characters in body; edited title Mar30 asked Example of $H^n(X,R)$ not equal to $Hom(H_n(X,R),R)$ Mar30 comment Finding joint probability from double marginals note: cross-posted to MO mathoverflow.net/questions/201485/… Mar30 revised Finding joint probability from double marginals edited tags Mar16 asked Disintegration of probability measures, reference request Mar16 comment Cross Product Intuition Answer to 1: yes! That's why it only works in three dimensions, and in the general case you use the "exterior product" (look it up!). Mar16 asked Finding joint probability from double marginals Mar11 comment Maximum entropy distribution given second order marginals In this case a constant 1/8 distribution is the max entropy solution...but I have no clue in the general case! Mar11 comment Maximum entropy distribution given second order marginals Three binary variables $x,y,z$, take $p=1/4(\delta_{000}+\delta_{011}+\delta_{101}+\delta_{110})$. where $\delta_{xyz}$ is a peak at the position $xyz$. Visually, it is the 3D equivalent of "chess". It's easy to see that the double marginals are all constant. Mar11 comment Maximum entropy distribution given second order marginals There always exist a distribution which has all the same double marginals, namely the original $p$. And possibly some other...among which we take the one with the highest entropy. If it were impossible to find others, it would mean that the double marginals determine $p$ uniquely, which is absurd. Mar11 comment Maximum entropy distribution given second order marginals Why? Just take a lower entropy. Mar11 asked Maximum entropy distribution given second order marginals Mar2 comment What is the formula and the name of the mathematical-phenomenon seen at the ending of “Around the World in Eighty Days”? Beat, as in wave physics? Mar1 comment What is the variance of self-information (or surprisal)? Oh yeah sorry, thanks for the corrections. Feb27 asked What is the variance of self-information (or surprisal)? Feb21 answered preservation of the curvature tensor implies preservation of the connection?