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What counts as having reproduced a published result?

A genuine question about practice rather than about a calculation. We re-ran an analysis from a paper using our own pipeline and got a number that agrees within the quoted uncertainty, but our…

When does a spectral gap imply exponential mixing?

问题维基

For a reversible Markov chain on a finite state space, a spectral gap gives exponential decay of the variance, and the constant is explicit. The statement I keep seeing quoted for the non-reversible…

Differentiating through an eigendecomposition with near-degenerate eigenvalues

The standard backward rule for a symmetric eigendecomposition has in it, which is fine right up until two eigenvalues approach each other. In our case they approach each other exactly where the…

Preconditioner that works to 512 cores and falls apart at 1024

Strong scaling is close to ideal up to 512 ranks. At 1024 the iteration count roughly doubles and the wall time goes up. The partitioning is the same algorithm at both sizes and the subdomains are…

Sampling a transition that happens once in a billion steps

Direct simulation will not reach it, and the usual enhanced-sampling machinery wants a reaction coordinate I do not have — the transition is collective and every one-dimensional coordinate I have…

Is a cache-oblivious stencil still worth it on current memory hierarchies?

The classic results are from machines with a very different ratio of bandwidth to compute. On our current nodes a straightforwardly blocked stencil with tuned tile sizes is beating our…

Table 3 is off by a factor of two pi and the text is not

Either the table or the text is wrong, and they cannot both be right. The text gives the coupling in angular frequency and the table's caption says the same, but the values are consistent with…

Notation for an average over configurations of an average over sources

This is a writing question and I am asking it anyway, because the last three manuscripts I refereed each invented their own and I could not follow any of them. The quantity is an average over gauge…