I've had a hard time trying to find hard figures on these numbers, and am trying to steer as much from speculation as possible.
Your second observation is a very good one. This is true, e.g. for the default intervention. Adding initial infections has a similar effect to waiting, and delaying an intervention can have a tremendous effect (at least according to the model) on the course of the epidemic
See the literature on exact penalty methods. I believe the short of it is yes, for a large class of problems this works, but the new problem will not be necessarily easier to solve. In the case of the abs(.) function, the nonlinearity at 0 makes subgradient methods slow, and the large constant in front of the abs(.) might prove numerically unstable.
I guess the author is not claiming a well rounded (low bias) introduction to ML to statistics, but a highly biased and specialized (low variance) course that is tailored to the author's own interests and tastes.
the illustration shows 4 an approximation with quadratic curves. There's no point drawing the one with 8 as it would be indistinguishable, as the article points out
I don't think so. This effect, at least as described, can change even as the phone remains static, e.g. if you head moves while the phone sits still on the table.
Sure, those terms are used in the paper. In general, open-loop vs. closed-loop refer to systems without and with feedback, respectively. Previous studies already showed that high-frequency stimulation could improve memory. Those were open-loop because they didn't use EEG feedback; stimulation is always on. The alternative is stimulation only when the subject is predicted to forget the word, based on EEG feedback.
The obvious question is whether EEG-based stimulation makes any difference compared to always-on stimulation. It is very possible that the difference is negligible and that the EEG feedback doesn't matter.
A simple example of this that has been shown rigorously is compressed sensing. Finding the sparsest vector, subject to linear constraints Ax = b is NP hard for general matrices, but is solvable in polynomial time if A satisfies the RIP property (e.g. w.h.p if A is generated by randomly sampling gaussians for each entry). Quite surprising!
Another example (that may be related to yours) is the general linear programming problem, that is, for vector x,
max c^T x
s.t. A x <= b [component-wise]
If problem instances (A, b) are chosen at random, from a rotationally-symmetric distribution, Borgwardt and others showed that, with high probability, the number of steps of the solution method is bounded by a polynomial in the number of dimensions. But on the other hand, there are explicit constructions of (A, b) that cause an exponential number of solution steps.
The usual interpretation is that "most" problems are friendly to the standard linear programming approach, but a few are not.
default values are the best guesses for the parameters of the novel coronavirus based on my reading of the literature