quantum theory is a hypothesis. perhaps it's the best one so far for what the brain is made from. but it's truth is only as demonstrable as this: it's not yet been falsified.
if you want to build a reliable system, one useful thing to do is use equipment from multiple vendors. sure it's inconvenient, but by doing this you can often de-correlate failures. especially if you want to improve someone else's reliability.
e.g., from simple things like hard drives in a raid from different vendors, to n-version programming in safety critical systems (like airplanes).
i wonder if you are thinking of another monoid property of a gaussian?
suppose we have:
x ~ N(0,1)
y|x ~ N(x, 1)
then we have:
y ~ N(0, 2)
i.e., gaussians are closed under marginalization.
however, i believe gaussians are not the only distribution with this property either: i think this property corresponds to the stable family of distributions: https://en.wikipedia.org/wiki/Stable_distributions
all exponential family distributions may be written in a form that depends upon a set of fixed dimension sufficient statistics.
https://en.wikipedia.org/wiki/Exponential_family
these sufficient statistics have the additive form described in this article (this is a consequence of i.i.d. sampling).
it is common to exploit this structure when implementing efficient inference in, for example, mixture models.
if you combine this property with a bayesian analysis, and put a conjugate prior on the parameters of an exponential family distribution, then the posterior distribution, and the marginal likelihood depend upon on the data only through these sufficient statistics and everything else is easily computed. in this form, one of the sufficient statistics often has an interpretation as a "pseudo-count"; how many effective samples are encoded in your prior?
exponential family distributions include: poisson, exponential, bernoulli, multinomial, gaussian, negative binomial, etc.
these torrent sites seem to have a business model that makes them money, even a profit. what prevents larger media companies from adopting this proven(?) business model?
the bsd license says: "Redistributions in binary form must reproduce the above copyright notice, .... in the documentation and/or other materials provided with the distribution."
i'm a bit confused: the bsd license allows you to re-sell someone else's source, binaries, images, etc for a profit. you just have to include the copyright notice.
is that what you're sending the dmca notice about? because you couldn't find the necessary copyright notice? (if you didn't download it, how do you know it's not in the about box?)
you can't really account for academic time on a hours-per-week basis. there's too much variety. as others have noted, it's a modal way of working. one week it's this, next month it's this, then maybe there's a paper deadline so you have to crunch down and get on a particular project. maybe it didn't fly so you have to try something else. it also depends where your university is.
being a professor is like running a company but with fewer support staff.
running your lab takes time most weeks, it's almost a constant: whole-lab meetings are easily 2-3hours per week, meeting each individual member of your lab is another hour or so each. then there's the admin for your lab (some of which you delegate). then there's organizing new grants: this involves collaborating with other people which means... yup, more meetings, often over skype or similar. then working out ideas, then writing, re-writing, and re-writing the draft and doing a lot of preliminary work. many grants need a lot of preliminary work to be shown before they get funding.
teaching is a lot more than just lecturing, you forgot: time spent talking to students one-on-one, running labs, designing interesting homeworks and exercises, preparing exams, marking homework and exams (marking easily consumes a week or two per course here).
also, "knowing stuff already" doesn't mean you can teach it. it's enough to teach yourself, not others. developing a new course or just keeping and old course up to date and interesting takes an awful lot of time. what content will you include? what exercises? what text books? what's examinable? what's useful? what's the structure? what can students handle? all of these apply to courses old and new, but are faster for older courses, especially ones that do not change much (i.e., not active research areas).
then there's your research. what you do here depends upon the stage of you career. in the very least, you need to read. a lot. in CS-disciplines, this is easily a weekly activity. then you can spend some time thinking. then trying some things out. maybe. then going to conferences, talking to more people. presenting your own work: writing papers, arguing about their acceptance, visiting labs, workshops and conferences to give talks, preparing talks, etc.. believe it or not, you have to advertise and advocate your research, even once it's published and done. how else will people notice? so advertising is another thing you must spend your time on.
now multiply all this work by the number of projects you have: potentially one per lab member.
interestingly you miss out one of the most important parts of being an academic--reviewing other people's work for conferences and journals. this takes a lot of time. firstly because reviewing a paper thoroughly takes considerable time, secondly because the discussion afterwards takes considerable time, and thirdly because often you will do this many, many times a year. as you become more senior, you take on a more senior role here: managing reviewers, journal and proceedings, conferences and workshops, etc.
i'm sure this isn't the same everywhere, but this is a small glimpse at academia in the places i'm aware of. it's busy busy busy.
i think you might have misunderstood what i wrote. i didn't say artists make more money from spotify/last.fm. i said they got a higher proportion of what was paid.
either way, it sounds like there are just anecdotes on both sides, so there's no actual information either way.
i think it can be pretty tricky to get real intuition without having the maths around. for example: exactly what assumptions do these methods make about the kinds of noise in the data? this can make a large difference in practice.
interestingly, with spotify and last.fm, artists get a higher proportion of the total money (15.3% and 15.8%, respectively) than they do with amazon/itunes (14.5%). it's surprising to me that it's so low for the artist in these cases.
there is not a normative way to discriminate between those two predictions.
it comes down to what kind of loss you incur for making an incorrect prediction. for mean, it's a squared loss (which penalizes you for being wrong in the tails more heavily) but for a median it's the absolute loss.
the argument being made was that fb is an outlier and (as I read it) the mean didn't reflect it, so the maths was "lazy" as it didn't take that into account. actually the mean does take these outliers into account (since it's corresponding loss function penalizes you harshly for being wrong in the tails) and so is probably not too unreasonable at predicting on outlier companies (certainly better than the median).