I'm looking into some PPL (probabilistic programming language) stuff, and as part of that I'm trying to come up with approximations of the results of various functions applied to distributions. For instance, let's say I want to apply the sigmoid function 1/(1+e-x) to a normally distributed random variable. We can solve for the cdf of this distribution by feeding the inverse of the sigmoid through the cdf of a normal distribution. From this we wind up with a reasonably complicated distribution on (0, 1). I'd like to estimate this distribution with a beta distribution, but I have no idea how to go about it. Although I have an expression of the pdf of the resulting distribution, I cannot even calculate the expectation value of it. Outside of SVI or Monte Carlo methods is there a way to calculate this?
I must admit that rather than clarifying, this discussion only made me more confused about whether my original assertion is "correct" or not.
On the other hand, worrying about 8 GB of disk space? What year is this?
(In actual reality, the force you feel due to acceleration is parallel to the direction of acceleration, whereas the force due to a massive body is radial to the body, so you will experience tidal forces which can be detected (if the body is under you, then your feet experience slightly lower acceleration than your head, so you are stretched by this imbalance of forces, and the force on your left arm is down and to the right, whereas the force on your right arm is down and to the left, squeezing you slightly left to right.) However, if you were to construct an infinitely large flat massive surface then gravity and acceleration would be indistinguishable, even in principal.)
"The second most irrational number" would refer to the "most irrational" number that's not equal to those. I suppose one could come up with infinite patterns of 1's and 2's in the continued fraction representation, a simple example would be alternating between them. I suppose it could be argued to be "more irrational" than sqrt(2), because the continued fraction approaches that value slower than the one for sqrt(2). Out of curiosity I tried to solve what 1+1/(2+1/(1+1/(2+... equals to, and I got (1±sqrt(3))/2.
On that note, both argue that phi, ie. the golden ratio, is "the most irrational number". The latter video tangentially, and perhaps serendipitously, also gives an argument for what could be considered "the second most irrational number", which would be sqrt(2). (It's all about their continued fractions, and how fast they approximate the actual value.) Indeed, it appears that if you need a "very irrational number" (that has the properties that their continued fractions have), sqrt(2) seems like an easy and good choice.
I saw this on a t-shirt:Is that really so?
According to OEIS, the asymptotic behavior of ak(n) seems to be nk/kk. I do not know why this would be the case.
It should be noted that the behavior of a5(n) seems to exhibit non-monotonicity quite a bit.
OK, so I practiced the wall jump thing and sort of got the hang of it (that means failing nine times and getting it once), but the flagpole glitch is absolutely impossible. It requires a very exact landing spot, Xspeed and Yspeed, and also requires different controls on each frame (usually left+right, empty, right, Left+right+A, empty, right) which is impossible to be done in a real time speedrun.
In this Numberphile video Matt Parker proves that the ratio between consecutive Fibonacci numbers approaches the golden ratio. He does this by noting that the definition of the Fibonacci numbers is that each number is the sum of the two previous numbers, and then assuming that as we go along the sequence, the ratio between two consecutive pairs of numbers approaches the same value, ie, that Xn/Xn-1 = Xn-1/Xn-2, and then solves what that ratio must be so that the equality holds (which, of course, is the golden ratio). But isn't he just assuming that the ratios of consecutive Fibonacci numbers converges to a particular value? He is also assuming that the ratios of two consecutive pairs approach each other as we advance in the sequence. On which basis can these assumptions be made? Couldn't it be perfectly possible that the ratios diverge, or oscillate, as we go along the series? Can the convergence simply be assumed? Shouldn't it be proved?
It also has a cool, optional, automated sub-level that's fun to watch at least once. I figure if I'm going to make an impossible level, I might as well put on a show! You can additionally check out previous versions of the level in my profile, but they aren't nearly as polished, and also can be cheesed to varying extents in order to clear them.
* 99.999999999999999999999999875664384% guaranteed! (Not a joke.)Wouldn't the any% be more like this this though: [1205] NES The Legend of Zelda "2nd quest" by Baxter & Morrison in 24:59.83 Which may make it somewhat redundant?
That got me thinking. Since there's already a 2nd quest category, a swordless and also a 100%ish, would it be fair that a warped route obsolete the any%? Mind you, the any% route also has the "heavy glitch abuse" tag too.
Can someone recognize where the music in the first 20 seconds of this VOD from twitch is from? I swear for my life that I've heard it before, but I can't find it anywhere. Any help would be greatly appreciated.
The only thing that article tells me is that "yes, using the term in this context is a misnomer".
It's common to use the term "non-euclidean geometry" in video games where the level geometry does not follow logical physics. For example you are seemingly inside a close room with a column at its center, but if you walk around the column you end up in a completely different place (typically there's some kind of "portal" surface at one side of the column that connects the level to another completely different level.) For example the game Antichamber is based on this. Is "non-euclidean geometry" a misnomer in this case? It doesn't sound like a case of hyperbolic or elliptic geometry.
