Super rough summary of the first half: in order to pick out random vectors with a given shape (where the "shape" is determined by the covariance matrix), MASS::mvrnorm() computes some eigenvectors, and eigenvectors are only well defined up to a sign flip. This means tiny floating differences between machines can result in one machine choosing v_1, v_2, v_3,... as eigenvectors, while another machine chooses -v_1, v_3, -v_3,... The result for sampling random numbers is totally different with the sign flips (but still "correct" because we only care about the overall distribution--these are random numbers after all). The section around "Q1 / Q2" is the core of the article.
There's a lot of other stuff here too: mvtnorm::rmvnorm() also can use eigendecomp to generate your numbers, but it does some other stuff to eliminate the effect of the sign flips so you don't see this reproducibility issue. mvtnorm::rmvnorm also supports a second method (Cholesky decomp) that is uniquely defined and avoids eigenvectors entirely, so it's more stable. And there's some stuff on condition numbers not really mattering for this problem--turns out you can't describe all possible floating point problems a matrix could have with a single number.
The idea is that memory-only data systems like HyPer are able to make design decisions that make them significantly faster that disk-based systems (eg postgres), even when the working set fits entirely within cache for the disk-based system. Umbra attempts to act like an in-memory DBMS when the working set fits in memory while degrading gracefully as the working set grows beyond memory. Agree the title doesn’t have enough detail to see this though.
There's a lot of other stuff here too: mvtnorm::rmvnorm() also can use eigendecomp to generate your numbers, but it does some other stuff to eliminate the effect of the sign flips so you don't see this reproducibility issue. mvtnorm::rmvnorm also supports a second method (Cholesky decomp) that is uniquely defined and avoids eigenvectors entirely, so it's more stable. And there's some stuff on condition numbers not really mattering for this problem--turns out you can't describe all possible floating point problems a matrix could have with a single number.