Given that you're citing Wikipedia on this, the issue of detecting and fighting auto-generated slop in articles is actually quite fascinating.
There was a really interesting talk given by Mathias Shindler (long time editor of German Wikipedia) at the 39C3 conference about this topic a few months back that is worth a watch for anyone interested in the issue: https://youtu.be/fKU0V9hQMnY
Deepseek is a private corporation funded by a hedge fund (High-Flyer). I doubt much public money was spent by the Chinese state on this. Like with LLMs in the US, the people paying for it so far are mainly investors who are betting on a return in the long to medium term.
Sure, but the alternative is not really any better: if the choice is between being the guy who got it wrong vs. being the guy who got it wrong _and_ being the guy who persisted in throwing good money after bad, surely the former is prefereable. As far as I see, the fact that they keep going indicates that they genuinely still believe Copilot could pan out and become profittable in the long run.
Correcting for inflation (I used this tool by the US Bureau of Labor Statistics: https://www.bls.gov/data/inflation_calculator.htm), 30M USD in nov. 1995 would have a purchasing power equivalent to roughly 62M USD in feb. 2025. This is below half the budget of Moana 2 (150M USD, released in nov. 2024) for instance.
- The characteristic function of a random variable X is defined as the function that maps t --> ExpectedValue[ exp( i * t * X ) ]
- Computing this expected value is the same as regarding t as a constant and integrating the function x --> exp( i * t * x) with respect to the distribution of X, i.e. if X has the density f, we compute the integral of f(x) * exp( i * t * x) with respect to x over the domain of f.
- on the other hand: computing the Fourier transform of f (here representing the density of X) and evaluating it at point t (i.e. computing (F(f))(t) if F represents the Fourier transform) is the same as fixing t and computing the integral of f(x) * exp( -i * t * x) with respect to x.
- Rearranging the integrand in the previous expression to f(x) * exp( i * -t * x), we see that it is the same as the integrand used in the characteristic function, only with a -t instead of a t.
For those interested in looking slightly more into the characteristic function, it may be worth pointing out that the characteristic function is equal to the Fourier-transform (with the sign of the argument being reversed) of the probability distribution in question.
In my own experience teaching teaching probability theory to physicists and engineers, establishing this connection is often a good way of helping people build intuition for why characteristic functions are so useful, why they crop up everywhere in probability theory, and why we can extract so much useful information about a distribution by looking at the characteristic function (since this group of students tends to already be rather familiar with Fourier-transforms).
The variable n comes out of nowhere in theorem 3.3, and they do not refer to it in the proof itself as far as I can tell. Is this just an editing error (I think the formula 3.4 needs the variable n if f is multidimensional and we are integrating over R^n, but since f is in L^1(R) I'm not sure what it signifies. I am however worried that there's something I'm missing).
I suspect OP may have been going for a variation on the old "Programmer returns with zero eggs and 12 gallons of milk after having been asked to get one gallon of milk and if they have eggs to buy a dozen"-joke, but it falls flat in this instance since it relies on an interpretation bordering on deliberate misconstrual (i.e. applying the modifier "for each year of service" to the whole phrase "16 weeks plus two additional weeks" rather than just to the latter fragment "two additional weeks").
There was a really interesting talk given by Mathias Shindler (long time editor of German Wikipedia) at the 39C3 conference about this topic a few months back that is worth a watch for anyone interested in the issue: https://youtu.be/fKU0V9hQMnY