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In this report we provide an improvement of the significance adjustment from the FA*IR algorithm of Zehlike et al., which did not work for very short rankings in combination with a low minimum proportion $p$ for the protected group. We show how the minimum number of protected candidates per ranking position can be calculated exactly and provide a mapping from the continuous space of significance levels ($alpha$) to a discrete space of tables, which allows us to find $alpha_c$ using a binary search heuristic.
About 160 years ago, the Italian mathematician Fa`a di Bruno published two notes dealing about the now eponymous formula giving the derivative of any order of a composition of two functions. We reproduce here the two original notes, Fa`a di Bruno (18
In this work, we define and solve the Fair Top-k Ranking problem, in which we want to determine a subset of k candidates from a large pool of n >> k candidates, maximizing utility (i.e., select the best candidates) subject to group fairness criteria.
We propose an effective model of strongly coupled gauge theory at finite temperature on $R^3$ in the presence of an infrared cutoff. It is constructed by considering the theory on $S^3$ with an infrared cutoff and then taking the size of the $S^3$ to
In this note, we adapt the procedure of the Long-Moody procedure to construct linear representations of welded braid groups. We exhibit the natural setting in this context and compute the first examples of representations we obtain thanks to this met
In a recent paper by L. A. Bokut, V. V. Chaynikov and K. P. Shum in 2007, Braid group $B_n$ is represented by Artin-Buraus relations. For such a representation, it is told that all other compositions can be checked in the same way. In this note, we support this claim and check all compositions.