On top of this, it doesn't seem to be all that well done. When I use the map it's inconsistent about loading all data points when there are a lot of them. Put it on a 5 mile radius and search 7 days, then drag the map around a bit. A few more crimes usually appear.
And, of course, stats in hand, what pharmaceutical companies really do is bribe starving med students and residents with food, in exchange for the opportunity to advertise their medicines, which invariably works often enough.
So in the actual infinite limit, you've got a finite-sized error at the discontinuity happening over an infinitesimal range. Whether this "counts" as an error (since the integrated error over all points is zero; it's not like a Dirac delta) depends on your discipline, I think.
In physics (and I imagine engineering, etc.) we tend to ignore stuff like this, since "true square waves" don't really exist.
I'm sorry, but this is nonsense. Your explanation of what happens in successive partial sums is correct, but in the "actual infinite limit", what happens depends entirely on what you mean. Different senses of convergence mean different things.
Even in applications it's important to identify what sort of convergence is relevant to your needs and interests. Engineers certainly do not ignore this stuff, and I'd be surprised if all physicists really did. It's an important consideration in image processing and computational PDE, as, for example, things like the Gibbs phenomenon make it difficult to get good resolution of sharp edges if you try to use Fourier series. Not caring how a series converges could cost you orders of magnitudes in computational time to get the image resolution you want. You've heard of wavelets, I presume? It doesn't matter that square waves "don't exist". Tons of money gets poured into studying these things because things which behave in much the same way do exist. To a mathematician, of course, it's a simple, interesting example that suggests deeper ideas about Fourier transforms. If you like, you can leave it at that.
I'd say it's not exactly correct to say that the overshoot "remains there in the limit". The limiting behavior all depends on your definition of convergence. In some senses, the limit of the partial sums of the Fourier series exists and may be equal to the actual function. In others, the limit might not exist. For a square wave, here are a few examples:
- Pointwise, the Fourier series converges everywhere except at the point of discontinuity. There, it converges to the average of the left and right limits. In this sense there's no overshoot in the limit.
- In root mean square norm (L^2 norm), the Fourier series converges. i.e. The integral of the square of the absolute value of the error between the partial sums and the actual function goes to 0. In this sense, there's also no overshoot in the limit.
- In the uniform norm, the Fourier series does not converge. i.e. For some fixed error epsilon, there is always some point where the error between the partial sum and the actual function is at least epsilon. As stated in the article, a priori this property isn't anything special. It is impossible to uniformly approximate any discontinuous function by any sequence of continuous functions. Now, the Gibbs phenomenon is more, because not only do the partial sums not converge uniformly, but they always overshoot the left and right limits by a fixed amount. You can't say really that something happens "in the limit" because the limit does not exist. However, the limit fails to exist in an interesting way.
You can certainly get a discontinuous function being the sum of sines and cosines, as in this example.
The article looks entirely correct to me as is. I think any exposition is going to sweep some things under the rug, so I wouldn't worry too much if not all the details are fleshed out.
To discourage the opposition. A sudden uptick in polling can trigger a wave of support for some other party. Maybe they feel that a slightly fishy election can be dealt with more readily than a strong showing by another party.
Rigging elections means fake votes are cast in your favor. Assuming that overall turnout had no correlation with political preference to begin with, regions with higher turnout would correspond to places where more fake votes were cast. If most fake votes were for Yedinaya Russia, you would see correlation between turnout and their vote share, which you do.
Of course, more data is necessary to make the case. One ought to show that voter turnout shouldn't correspond to political preference.
As some see it, the main reason blackboards are used in math/physics is to get the teacher to slow the hell down. The only outcome of technology is teachers who fly through equations too fast for students to copy them.
Not everyone checks Slashdot religiously. It's nice that there's some repetitiveness. You see things you'd miss otherwise. I, like many others, am interested in accumulating a picture of what it is MS does that makes people call them evil.
Moreover, skipping a post you'd rather not read is trivial. Missing out on a topic you'd like to know more about is tragic.
Why do you want a static version of Wikipedia? Isn't it easier just to access the actual Wikipedia, which is constantly being updated? I often rely on the assumption that someone will have instantly posted about recent events. Naturally there are practical uses for good compression, but as fer usin' the darn thing, seems like the original is best.
I don't think it has anything to do with Russian psychology. Repetition as an intensifier is a well-grounded notion in linguistics, so many )'s makes it a big smile. Anyone could of thought of it. Whoever did seems to have been Russian (or Eastern European of some other sort).
Personally, my position is that media should be allowed to be copied and shared freely, so long as it is done noncommercially.
Doesn't it then follow that YouTube is allowed to commercially facilitate individuals' noncommercial sharing of media? I think it's intrinsic to Viacom's case that they own the content. If it's okay to share media, how is it not okay for YouTube to provide a service making it easier to share media, and to profit off of the ad revenue? The allegation is that they profit off the content itself, not the mere fact of the service they provide.
Viacom's content apparently isn't what continues to drive YouTube. YouTube's traffic doesn't seem to have been affected much by Viacom pulling its content, though it may take a while to tell. Offhand I'd say whatever profit YouTube may have gotten from of copyrighted content is done with. The site is now the established video vault, and it seems to be getting along fine (so far) without Jon Stewart.
Who actually listens to someone without double-checking their credentials? Least of all on a Wikipedia discussion page. Anytime someone purports to be an academic authority I Google them and check their publication list. People just need to get in the habit of not trusting anything they read (anywhere). It's basic internet instinct.
What I'm curious about is whether bandwidth usage will reach a natural saturation level in the long run. Hypothetically, it makes sense that there is some limit to how much video a person can watch (limited by time), some maximum quality level of audio/video that people will demand (limited by human senses), and some maximum storage that is feasible (limited by cost/power supply). All this ought to put an absolute cap on the total bandwidth use one could expect people to demand. It could be quite a bit greater than where we are now, but it doesn't seem out of the question that we could one day have a more or less perfect network.
Of course you make the assumption that it was a legion and not some other social unit including women. In any case they might as well test everything they can.
I also seem to remember from my high school history class that during the Meiji Restoration, when the Japanese decided to model certain institutions after those of whatever Western country was best at it (e.g. the British Navy, the German Army), they chose the American education system to imitate. Pretty counterintuitive these days.
Slashdot Mirror
On top of this, it doesn't seem to be all that well done. When I use the map it's inconsistent about loading all data points when there are a lot of them. Put it on a 5 mile radius and search 7 days, then drag the map around a bit. A few more crimes usually appear.
And, of course, stats in hand, what pharmaceutical companies really do is bribe starving med students and residents with food, in exchange for the opportunity to advertise their medicines, which invariably works often enough.
Please-God-Dont-Let-A-Gamma-Ray-Burst-Destroy-Us-All-Please-Please-Please-Im-Sorry Array.
So in the actual infinite limit, you've got a finite-sized error at the discontinuity happening over an infinitesimal range. Whether this "counts" as an error (since the integrated error over all points is zero; it's not like a Dirac delta) depends on your discipline, I think.
In physics (and I imagine engineering, etc.) we tend to ignore stuff like this, since "true square waves" don't really exist.
I'm sorry, but this is nonsense. Your explanation of what happens in successive partial sums is correct, but in the "actual infinite limit", what happens depends entirely on what you mean. Different senses of convergence mean different things.
Even in applications it's important to identify what sort of convergence is relevant to your needs and interests. Engineers certainly do not ignore this stuff, and I'd be surprised if all physicists really did. It's an important consideration in image processing and computational PDE, as, for example, things like the Gibbs phenomenon make it difficult to get good resolution of sharp edges if you try to use Fourier series. Not caring how a series converges could cost you orders of magnitudes in computational time to get the image resolution you want. You've heard of wavelets, I presume? It doesn't matter that square waves "don't exist". Tons of money gets poured into studying these things because things which behave in much the same way do exist. To a mathematician, of course, it's a simple, interesting example that suggests deeper ideas about Fourier transforms. If you like, you can leave it at that.
I'd say it's not exactly correct to say that the overshoot "remains there in the limit". The limiting behavior all depends on your definition of convergence. In some senses, the limit of the partial sums of the Fourier series exists and may be equal to the actual function. In others, the limit might not exist. For a square wave, here are a few examples:
- Pointwise, the Fourier series converges everywhere except at the point of discontinuity. There, it converges to the average of the left and right limits. In this sense there's no overshoot in the limit.
- In root mean square norm (L^2 norm), the Fourier series converges. i.e. The integral of the square of the absolute value of the error between the partial sums and the actual function goes to 0. In this sense, there's also no overshoot in the limit.
- In the uniform norm, the Fourier series does not converge. i.e. For some fixed error epsilon, there is always some point where the error between the partial sum and the actual function is at least epsilon. As stated in the article, a priori this property isn't anything special. It is impossible to uniformly approximate any discontinuous function by any sequence of continuous functions. Now, the Gibbs phenomenon is more, because not only do the partial sums not converge uniformly, but they always overshoot the left and right limits by a fixed amount. You can't say really that something happens "in the limit" because the limit does not exist. However, the limit fails to exist in an interesting way.
You can certainly get a discontinuous function being the sum of sines and cosines, as in this example.
The article looks entirely correct to me as is. I think any exposition is going to sweep some things under the rug, so I wouldn't worry too much if not all the details are fleshed out.
To discourage the opposition. A sudden uptick in polling can trigger a wave of support for some other party. Maybe they feel that a slightly fishy election can be dealt with more readily than a strong showing by another party.
Rigging elections means fake votes are cast in your favor. Assuming that overall turnout had no correlation with political preference to begin with, regions with higher turnout would correspond to places where more fake votes were cast. If most fake votes were for Yedinaya Russia, you would see correlation between turnout and their vote share, which you do. Of course, more data is necessary to make the case. One ought to show that voter turnout shouldn't correspond to political preference.
Actually when /. articles have 700 comments or so I need to answer the "script not responding" error message several times.
As some see it, the main reason blackboards are used in math/physics is to get the teacher to slow the hell down. The only outcome of technology is teachers who fly through equations too fast for students to copy them.
Not everyone checks Slashdot religiously. It's nice that there's some repetitiveness. You see things you'd miss otherwise. I, like many others, am interested in accumulating a picture of what it is MS does that makes people call them evil.
Moreover, skipping a post you'd rather not read is trivial. Missing out on a topic you'd like to know more about is tragic.
Why do you want a static version of Wikipedia? Isn't it easier just to access the actual Wikipedia, which is constantly being updated? I often rely on the assumption that someone will have instantly posted about recent events. Naturally there are practical uses for good compression, but as fer usin' the darn thing, seems like the original is best.
or H2O, NH3, C2H5, PDQU235 and a pinch of salt
The difference is that the North Pole is currently unclaimed, and apparently there's some UN protocol saying when you can claim unclaimed territory.
I don't think it has anything to do with Russian psychology. Repetition as an intensifier is a well-grounded notion in linguistics, so many )'s makes it a big smile. Anyone could of thought of it. Whoever did seems to have been Russian (or Eastern European of some other sort).
Personally, my position is that media should be allowed to be copied and shared freely, so long as it is done noncommercially.
Doesn't it then follow that YouTube is allowed to commercially facilitate individuals' noncommercial sharing of media? I think it's intrinsic to Viacom's case that they own the content. If it's okay to share media, how is it not okay for YouTube to provide a service making it easier to share media, and to profit off of the ad revenue? The allegation is that they profit off the content itself, not the mere fact of the service they provide.
Viacom's content apparently isn't what continues to drive YouTube. YouTube's traffic doesn't seem to have been affected much by Viacom pulling its content, though it may take a while to tell. Offhand I'd say whatever profit YouTube may have gotten from of copyrighted content is done with. The site is now the established video vault, and it seems to be getting along fine (so far) without Jon Stewart.
Who actually listens to someone without double-checking their credentials? Least of all on a Wikipedia discussion page. Anytime someone purports to be an academic authority I Google them and check their publication list. People just need to get in the habit of not trusting anything they read (anywhere). It's basic internet instinct.
What I'm curious about is whether bandwidth usage will reach a natural saturation level in the long run. Hypothetically, it makes sense that there is some limit to how much video a person can watch (limited by time), some maximum quality level of audio/video that people will demand (limited by human senses), and some maximum storage that is feasible (limited by cost/power supply). All this ought to put an absolute cap on the total bandwidth use one could expect people to demand. It could be quite a bit greater than where we are now, but it doesn't seem out of the question that we could one day have a more or less perfect network.
While Canada might be larger in terms of land area, ...
It's not, actually. The US has larger land area. Canada wins if you throw in water. By land area, the ranking goes:
Russia
China
USA
Canada
I've always wondered if this was done intentionally so that China would get pushed to 4th.
Of course you make the assumption that it was a legion and not some other social unit including women. In any case they might as well test everything they can.
I also seem to remember from my high school history class that during the Meiji Restoration, when the Japanese decided to model certain institutions after those of whatever Western country was best at it (e.g. the British Navy, the German Army), they chose the American education system to imitate. Pretty counterintuitive these days.
... and someone was kind enough to help them out a bit more with their traffic.
Better than e!
You mean \Gamma(e).