text:
# Approximating 1D integral with Metropolis - Hastings Markov Chain Monte Carlo

I've been asked to approximate the integral of a one dimensional unnormalised posterior with a flat prior, using a Metropolis Hastings Markov Chain Monte Carlo, I realise that this isn't a practical endeavour, i think its more of an instructional exercise.

At the moment, I am creating a Markov chain of sampling points, $\{x_i\}$, for the distribution using the MH algorithm, and then approximating the integral of the posterior as:

$$I \approx (\text{Prior interval}) * \frac{1}{N}\sum_i f(x_i)$$

where $f(x_i)$ is the likelihood evaluated at the point $x_i$ in the chain, and N is the length of the Markov Chain.

I have tested this algorithm in Python for numerous simple posteriors, and it converges on completely the wrong answer in every case. I've been over the code many times, and I'm almost certain there's nothing wrong with it. I also read that you need to discard the first half of the chain, and discard everything but every, say, 10th point. I've tried this and it makes no difference.

The code is shown below. It tries to integrate $\sin x$ between $0$ and $\pi$. For 20000 iterations it gives $2.45448671306 \pm 0.00502441977146$, which is obviously very wrong (answer should be 2) .The graph below shows the convergence of the algorithm

def f(x):
if 0. <= x <= np.pi:
return np.sin(x)
else:
return 0

n = 20000 #number of iterations
sigma = 0.5

x = uniform(0, np.pi) #initial x value

chain = [] #stores Markov chain
chain.append(f(x)) #initialises chain

accept = 0 #number of accepted jumps

#generates an array of random x values from norm distribution
rands = normal(0, sigma, n)

#Metropolis - Hastings algorithm
for i in range(1,n):
can = x + rands[i]  #candidate for jump
aprob = min([1., f(can)/f(x)]) #acceptance probability
u = uniform(0,1) #rand number between 0 and 1
if u < aprob:
x = can
accept += 1
chain.append(f(x))

I = (np.pi)*sum(chain)*(1/len(chain)) #integral approximation

#uncertainty on approx.
uncertainty = (np.pi) / np.sqrt(len(chain)) * np.std(chain)

#integral approx at each iteration
conv = np.array([(np.pi)*sum(chain[:x+1])*(1/(x+1)) for x in range(len(chain))])

print('MCMC approx: ', I, '\t','uncertainty: ', uncertainty)

• As discussed in this answer, using the posterior sample to approximate the marginal likelihood, ie the integrated unnormalised posterior, is not correct. You either need to use a prior sample or the posterior sample with a more convoluted estimate. I list a collection of solutions in this answer. – Xi'an Nov 29 '16 at 19:52
• Thank you for your reply, that answer works like magic! I'll have to go away and read up on why that works. However, the way the question was set, and from my lecture notes, suggests that I really should be able to tackle this problem just using the MH algorithm and the mean of the Markov Chain (we haven't covered anything more sophisticated than this, and aren't expected to). So are you sure that a simpler alteration to the algorithm can't fix it? And could you point me to some literature which explains why the mean of the markov chain wont give the integral? – oweydd Nov 29 '16 at 22:14
• Ok, so I've asked my lecturer and we weren't actually required to find the integral, just to sample from the posterior. Nonetheless, i think I've learnt something useful, so thank you. – oweydd Nov 30 '16 at 10:11
• There was a major mistake in your code, namely that you did not account for the rejections in the Metropolis-Hasting part. When a proposed value can is rejected the current value x needs to be replicated, as illustrated in my code. – Xi'an Nov 30 '16 at 10:19

"I've been over the code many times, and I'm almost certain there's nothing wrong with it."

There is an issue with the code, actually, in that you fail to replicate the current value of the Markov chain x when rejecting the candidate value can, while you should: thus the conditional update

   if u < aprob:
x = can
accept += 1
chain.append(f(x))

should be corrected as done in the R code below:

    if (u < aprob){
x = can
accept = accept+1}
chain=c(chain,f(x))}

Furthermore, there is a conceptual (and common) error in averaging the $f(x_i)$'s when the $x_i$'s are simulated from the posterior distribution, $g(x)\propto f(x)\mathbb{I}_{(0,\pi)}(x)$. Indeed, the expectation of a term in this average is$$\int_0^\pi f(x)g(x)\,\text{d}x=\int_0^\pi f(x)\times\frac{f(x)\mathbb{I}_{(0,\pi)}(x)}{\int _0^\pi f(x)\,\text{d}x}\,\text{d}x=\frac{\int_0^\pi f^2(x) \,\text{d}x}{\int _0^\pi f(x)\,\text{d}x}$$

Using the posterior sample as you do in the Monte Carlo approximation hence amounts to using the likelihood twice, i.e. integrating $f^2$ rather than $f$.

The Harmonic Mean Estimator

One immediate way to deduce an approximation of the integral$$\mathcal{I}=\dfrac{1}{\pi}\int_0^\pi f(x)\text{d}x=\dfrac{\cos(\pi)-\cos(0)}{\pi}=\frac{2}{\pi}$$ which is the marginal likelihood, is to use the sample $(x_i)$ from the posterior inside an harmonic mean estimate: $$\hat{\mathcal{I}}=1\big/\frac{1}{n}\sum_{i=1}^n \frac{1}{f(x_i)}$$This is a consequence of the identity$$\mathbb{E}[f(X)^{-1}]=\int_0^\pi f(x)^{-1}\frac{f(x)\mathbb{I}_{(0,\pi}(x)}{\mathcal{I}\pi}\text{d}x=\int_0^\pi\frac{\mathbb{I}_{(0,\pi}(x)}{\mathcal{I}\pi}\text{d}x=\frac{1}{\mathcal{I}}$$ The estimator returns an unbiased estimate of the inverse integral, but its major drawback is that it often has an infinite variance, hence is unreliable no matter what the number of simulations. Radford Neal has called this approach the worst Monte Carlo method ever and I concur. Only use it when you want to check that the value of the integral is what another approach tells you it should be. As in this exercise.

f <- function(x){
if ((0<x)&(x<pi)){
return(sin(x))}else{
return(0)}}

n = 2000 #number of iterations
sigma = 0.5
x = runif(1,0,pi) #initial x value
chain = fx = f(x)

#generates an array of random x values from norm distribution
rands = rnorm(n,0, sigma)

#Metropolis - Hastings algorithm
for (i in 2:n){
can = x + rands[i]  #candidate for jump
fcan=f(can)
aprob = fcan/fx #acceptance probability
if (runif(1) < aprob){
x = can
fx = fcan}
chain=c(chain,fx)}

I = pi*length(chain)/sum(1/chain) #integral harmonic approximation

Here is the corresponding result for n=1e5:

> I
[1] 2.000591

which coincides with the true value. Hence the harmonic mean did not hit too small a value of $\sin(x)$ to induce large variations in the average. But, nonetheless, $1/\sin(x)$ has an infinite integral on $(0,\pi)$ and the resulting harmonic mean estimator has an infinite variance.

An explanation for the surprisingly good performances of this "worst Monte Carlo method ever" is that sigma = 0.5 does not often return values of $\theta$ that are close to $0$ or to $\pi$. If instead one uses sigma = 0.01 in the above code, the result is quite different:

> I
[1] 3.039536

and highly variable

> I
[1] 0.5901059

Hence it cannot be trusted and should not be used.

The Metro-Hastings sampling procedure is over-sampling higher values due to the accept/reject criteria.

The average of the sample values returned by
sum(chain) * (1/len(chain))
is too high.

In typical method for Monte Carlo integration, random samples are drawn uniformly across the [0, pi] interval.

You can still use a Markov Chain to create "jumps". For example, changing

for i in range(1,n):
can = x + rands[i]  #candidate for jump
aprob = min([1., f(can)/f(x)]) #acceptance probability
u = uniform(0,1) #rand number between 0 and 1
if u < aprob:
x = can
accept += 1
chain.append(f(x))

to

for i in range(1, n):
x += rands[i]  #candidate for jump
if f(x) > 0:
chain.append(f(x))

will get a much better approximation


text:
# Optimum Re-entry Corridor for Apollo-type Spacecraft

1. Apr 9, 2013

### roldy

I'm working on a project in MATLAB for my own personal benefit. I found a 1966 paper where the limits of the re-entry corridor are found. The control variable is the attack angle. The state variables are flight path angle, velocity, altitude, angular displacement (range), and penalty functions for altitude and g-force loading on the pilot. As of now, trying to work the limits of the re-entry corridor. This is done by numerically integrating the equations of motion and checking to see if the total g-force loading on the pilot is above a threshold. The penalty function for altitude is there in case the spacecraft skips out above the reference altitude of 150 km. I'm not concerned with this part. The pilot penalty function was digitized and an equation was fit to the curve. This equation is in the numerical integration function.

Note: I tried two different sets of equations for the equations of motion. It seems that the second set is working better and I'm getting reasonable re-entry time values.

For the time being, I'm just testing out the program (without optimizing the reentry flight path angle) with a flight path angle of 90 degrees. To check if this part of the program is working, I plotted Altitude vs. range. The range they have goes from 0 to 1. My values are on the order of 10-5.

The sets of equations I am using are as follows:
$\dot{V} = -D/m+ g\sin(\theta)$
$\dot{\phi} = -V\cos(\theta)/(R_E + alt)$
$\dot{\theta} = (L/m - g\cos(\theta))/V$
$\dot{alt} = -V\sin(\theta)$
$\dot{Pilot_{pen}} = 1/\tau$
The function $\tau$ is in the code.

$g = g_{surf}(R_E/(R_E + alt))^2$
$\rho = 1.752e^{-alt/6700}$

$C_d = 2(\sin(\alpha))^3$
$C_l = 2(\sin(\alpha))^2\cos(\alpha)$

$D = 1/2C_d\rho V^2S_{ref}$
$L = 1/2C_l\rho V^2S_{ref}$

$Aero_{accel} = \sqrt{(L^2 + D^2)/(mg_{surf})}$

Could someone take a look at my code and see if I am doing anything wrong? Here is the link for the zip file containing the code and the paper I am working from.

Last edited: Apr 9, 2013

format: plain


text:
# An open letter to /merit/

This is a formal complaint to /merit/ regarding our current commissioner King Lear, and why the signers of this complaint believe he has failed the fundamental requirement of impartiality that is required of a commissioner and is thus unfit for the role. We believe these complaints are not personal attacks, but rather an attempt to recount some of the events that led us to believe that he is not fit for the role he currently occupies, and therefore must step down. Let's get started.

## Undue involvement with /w/

This is unfortunately the first point that must go out of the way in order to estabilish the lack of impartiality that Lear represents as a Commissioner.

During the 2017 Spring Babby Cup, /w/ was grouped with /a/, and had to face them in match 3 out of 3. Lear was then present in the public /a/ discord, and active. Goat, then manager of /w/, was absent.

Come gametime, then streamer Sou had to make substitutions for /w/'s team, and accidentally put a certain CB on the pitch despite being told not to do so in /w/'s pastebin. This promptly followed in /a/'s chat in the wake of the result:

[8:37 PM] Lear: Sorry it had to go down like this.
[8:37 PM] Lear: I wish Sou hadn't subbed on our smallest CB in the middle when the pastebin said specifically not to do that.
[8:39 PM] Lear: I'm too angry at Sou for costing the lead to be happy at this.

Already this raises a few questions: Why does the supposedly impartial commissioner know a pastebin of a team he was formerly manager of 2 years prior by heart? But most importantly, why would this matter when /w/ was coming into the match already relegated? I'll let him explain.

[8:44 PM] Lear: I'm angry because Sou just cost /w/ 17th place.

The Cull followed immediately afterwards and saw /w/ advance to summer until /w/'s nonexistent Proof of Interest posts came to light. The Commissioner had intended to use prior knowledge of the Cull to favor his own teams' chances of advancing, and was nearly stripped of the chance due to Sou's rigging. This is just the most egregious episode, but there's more. When /w/'s interest was put into the spotlight again in Autumn, Lear admitted to participating to /w/'s interest thread:

[12:02 AM] Two_Scoops: IIRC the reason he said he posted there to begin with was to put enough images in the thread to comply with /w/ rules
[12:02 AM] Two_Scoops: but that's not his job, it's the fucking manager's job
[12:06 AM] Lear: I posted in that thread because Goat asked me to get some pics of the team ingame as wallpapers. I figured it was easier to just post them myself then go through a broken telephone.

Why would the Commissioner need to fill in to post screenshots of PES, when /w/ had a manager that was supposedly active and in their fifth cup, and why would Goat need to ask him? I'll let him explain one more time, when talking about Spring 16:

[8:05 PM] Lear: Also I'm not the manager for /w/ anymore so I probably shouldn't sign them up for stuff.
[8:06 PM] Lear: Goat is real he just cannot into PES.
[8:10 PM] Lear: In Spring both teams that escaped the group were the ones that never tested.
[8:11 PM] Lear: Also the teams that had exports made by me. (note: the other is /trv/)

There is more, however, and this is where the rule about the commissioner not managing a team flies straight out of the window.

Lear has, on multiple occasions, admitted to testing for /w/, while the manager in charge was Anonymous Goat, more specifically during the 2017 Winter and 2017 Spring Cups:

[7:49 PM] Ramen: @CuriousAnon QD doesn't into tactics much
[7:50 PM] Ramen: its gw that does most of the dumb shit
[7:51 PM] Johnny: qd told me he wanted tight marking on the amfs and gw shot it down
[7:51 PM] Heavenly_Pond: Would that help
[7:51 PM] TheWorst: >GW
[7:51 PM] Johnny: Probably not
[7:51 PM] Ramen: qd said he wanted gw to not run hug the touchline and he never stopped(edited)
[7:52 PM] Johnny: /m/ outright manmarked them and still conceded 3
[7:52 PM] Lear: Yeah when I was testing against /vg/ they played better without their advanced instructions easily.

[5:59 AM] Lear: Everything about Welcrom (note: then an /a/ tester) I like.
[5:59 AM] Lear: He's even trying to help /w/.
[5:59 AM] rhs: except he doesn't go into pixel autism like NFR
[5:59 AM] rhs: >Welcrom is feeding tactics to both teams
[5:59 AM] rhs: genius
[5:59 AM] rhs: he will win an Elite
[6:00 AM] Lear: No I meant those tictacs would be a godsend for /w/.
[6:00 AM] Lear: If /a/ used them.
[6:00 AM] Johnny: damn lear with the mindgames
[6:00 AM] rhs: I bet Lear is just foxing
[6:00 AM] rhs: and he is SCARED
[6:00 AM] Ramen: Oh we tried them
[6:00 AM] Johnny: if i was playing /a/ with a three six fun theres very few /a/ setups that would worry me :sunglasses:
[6:00 AM] Ramen: For shits and giggles
[6:01 AM] Lear: I'll have you know I tested exclusively against that setup because I am in your heads.

So here we have a commissioner that has admitted to the following regarding his former team /w/:

• Posting in their PoI threads
• Judging said PoI thread's quality and without fail, deeming them good enough to compete
• Making exports for /w/, which retained the same tactics for a full year after his tenure as manager had ended (Autumn 2016 /w/ was the 4-4-1-1 it had always been under Lear)
• Following their games closely, having full knowledge of their tactical pastebin (enough to know which CB was shortest in a time frame of seconds)
• Most importantly, openly admitting to testing for the acting manager in spite of his position as Commissioner.

Not only does this unequivocally disqualify Lear from being an impartial party, it is also a de-facto violation of rule 3: The Commissioner may not manage a team during their tenure.

This is completely and utterly unacceptable, and the continued proxy managing of his former team alone should disqualify him from the role of commissioner, as it breaks the fundamental bond of trust managers are supposed to have towards the Commissioner, and there has already been at least one episode where Lear could have taken advantage:

On the 19th of May of 2017, f4r went missing in action after the deadline for matchday 4 of the Spring Babby.

Lear had to fill in for f4r's duties and made the EDIT file of a matchday where the team he was then proxy manager of played, and he got to handle a nightly export of the team /w/ was playing next. He then casually went on to comment in public on how his testing against /a/ went.

As an aside, I would also like to point out that this is now a renewed concern, as /w/'s Spring tactics will be made by someone that is not a "neutral party", by his own admission.

## Moving the gay goalpost and lack of standards

The new autopilot format has had, to date, two successful users: /cm/ and /p/. You'd think these two teams would then have a very similar story with interest and polling, and you'd be so crucially wrong.

As you all know by now, /cm/'s autumn poll was ran and supervised by Dragonfag, and they were ultimately allowed to play, as their interest was deemed legitimate. When /merit/ called this into question, the burden of proof to disprove the interest was legitimate (and not votes for a collection of DF's husbandos) was squarely placed on them, something that, with obvious reasons, they couldn't do.

I ran a preliminary strawpoll for /p/, which was approved by /merit/ (as opposed to /cm/ just coming in with interest). Given the green light, I polled /p/, and some 48 hours into the Autumn poll, some wonderful person decided to leak it to /4ccg/. I had to rush close the poll, and was then pre-emptively asked to prove no votes came from /4ccg/, and I was happy to oblige. The burden of proof was placed on me.

This however left the music selection for /p/ so close that I wasn't prepared to call the will of the board, so I decided to run a second, tiebreaker poll. This saw no complaints, and people were happy to vote and decide a winner. 14 of the 17 initial votes came back in a comparable time frame, and nothing of note has happened since. /p/ keeps being mildly interested and I keep wanting to build them.

Why is this tiebreaker poll relevant? /cm/ was going to be asked to do the same, after /cm/'s roster was given the green light by a couple of /cm/ browsers, as a way to unequivocally verify their interest as legitimate (the second poll would have been run by /merit/, ruling out any ballot stuffing that is possible with google polls), and the arguments Lear had against it, I find truly baffling and nonsensical when /p/ was able to vote twice without any doomsday scenario of the sort occurring.

Refer to Appendix 1 for the log.

Again as you know, the situation was ultimately resolved with calls of "let /cm/ play" with little criticism coming from the crowd, despite lacking any amount of information other than "DF made the poll but it is legitimate". It was then agreed that a banned person could never run a poll again, giving /cm/ preferential treatment and authorization to break the rules "just this once" on account of strong interest.

After this point, the discussion about /w/ happened, and Lear stopped answering to my enquiries about /p/. I had asked him about keeping a couple of no-aesthetics players out, and never got a response. I decided to ask then-recently out of /merit/ DescendingBear and other /merit/ members about the autopilot rules. I was unofficially told by DB that autopilots ought to require a thread every single cup cycle, before or during. Or do they?

/cm/ had a single winter thread that was linked on the stream's chat by SDA at zero replies, and then continued seemingly normally. Nobody had to prove their interest was legitimate, despite the fact that it was leaked at the very start. No thread was made for Spring's preparation and the roster was not updated. Despite this, /cm/ get to play with Autumn's roster. This, to me, had the same coherence of a random number generator, so once again I asked about autopilot interest:

[11:07 PM] Free my nigga megababby: So are we ever gonna write some rules down about autopilot and PoI or is it just gonna be wing it lmao
[11:08 PM] Free my nigga megababby: Cause /cm/ as far as I see from the archive is competing on Autumn PoI and until 2 months ago it was one cycle
[11:09 PM] Lear: And yeah we'll write out 1 cycle and all that.

So you'd think that this means that rules for autopilots are more lax now and they don't need a proper thread every cup cycle, but no later than 24 hours pass before he goes out of his way to defend the leaked thread that nobody can prove the legitimacy of.

Refer to Appendix 2 for the log.

Again, consider what is being said for a second here, just because /cm/ cannot, for some obscure reason, poll their board like everyone else:

• It is perfectly fine to violate the rules twice in a row and, in both instances, only give a vague and non binding promise to be harsher in the future rather than take any sort of decision right now
• It is perfectly fine for a team to compete on a roster that is years old, relying only on matchday threads made by people without any sort of relation to the cup, banned or not, and that are completely unverifiable in any way
• Being linked on stream, a location that is several magnitudes more visible than /4ccg/, where interest has been leaked and denied before is not enough reason to at least require another thread 3 months later
• It is perfectly fine for the only beneficiary of these decisions to be /cm/, while the other autopilots that are getting interested in the cup have to bust their ass and abide by the ever-changing, implied but not codified rules.

We have already seen the result of this inconsistency for the benefit of one team: /t/'s thread is a complete mockery of the current standards for autopilots, particularly /cm/ since the OP of both threads remains unknown and both got leaked, and the fact that /t/'s thread has been reported and deleted suggests there's an escalation that is potentially cancerous for the cup.

I don't really want a bunch of cross boarders to link my threads to 4ccg to then have them reported and deleted. It's not conducive to any small market and it screams of concerted effort to straight up kill any up and coming team.

## Not good enough for /u/

Lear went on First Bait, on the day after the round of 16 of the winter cup, and went on a completely unprompted huge, half hour long rant undermining /u/'s management ability and style of polling, while also slinging personal insults at him while being incredibly angry: https://www.smashcast.tv/firstbait/videos/1385699 - it starts at 35 minutes.

For context, this is the image Myuer posted in the chat: http://puu.sh/zYd1S/177ab33cb7.png - this is around the time of The Cull.

I will leave the footage to speak for himself, but do keep in mind that, as far as anybody I'm in contact with (/u/ management former and not) is concerned and going back as far as 2013, /u/ has always polled their meta thread, and has an agreement with the moderator to do so, while specifically being told not to create threads: https://4archive.org/board/u/thread/2001853#p2004050

Here's some choice quotes, just in case you can't watch the video:

"Maybe I'll be a bit kinder to them when they aren't filthy fucking casuals with garbage taste"

"...If you think you can justify the shit you pulled with that team, go ahead - [long rant about Citrus ensues] - no your garbage ass fucking general hates it, and you can't pull your dick out of your ass to see that!"

"I see only polling the general thread as basically rock bottom, because it's a fucking shithole"

"If you don't wanna take a 3 day, you don't give a shit!"

I honestly want to ask a question here, would you appreciate being under a magnifying scope for how you run the team you manage because the Commissioner doesn't like the general you have been confined in by the moderation, and ultimately questions your poll because of personal preference? Neither would I, but this blatant bias toward these teams seems like it's a repeated and well documented behaviour that shows no signs of ever getting better:

- His unwillingness to take /adv/'s signup over /wg/ in the 2016 Summer Cup, despite the fact /wg/ missed theirs and should have been immediately disqualified. /wg/'s participation remained in contention until most of the cup IRC and /4ccg/ complained, and he was forced to back down.

- Without dwelling too much on it, because plenty has already been said, his behaviour during and after The Cull, and his comments on /c/ and /u/ in particular.

The most egregious thing is that this is something that seems to have to do entirely with his own tastes, and not any genuine concern, and that he is actively calling to upset the moderation in order to start a thread when /u/ has specifically been told not to do so. Because clearly, what we need is more boards that are even less open about 4CC threads and more hostility from the moderation, whether you think it's good moderation or bad moderation.

I would also like to point out that being part of the 4CC organization shouldn't in any circumstance give you a higher standing than a 4chan moderator, whether you like them or not.

### This entire section is only for hurt feelings you freaking losers

Sargbot (talk) 21:26, 8 April 2018 (UTC)

## Lock before, explain later

The discussion on Spring's format has been, to put it simply, non-existent. /merit/ was, up until this week, aware of these new\revived team attempts: /3/, /aco/, /bant/, /hm/ and /w/, or in other words, exactly 40.

Given that all of these except /hm/ look like they're going to succeed, the smartest thing to do would have been announcing that we were very close to making a megababby happen (and possibly reviving managers that needed a little push - for example, /gif/'s former manager) and then waiting until the weekend to wrap up team making by including all of the teams that were in the stages of gathering interest, since he was already well aware of 40 interested teams being a more than real possibility.

This was suggested in /merit/, and it was promptly ignored. Lear then told /merit/ the blame was "on him" if people weren't satisfied with the current megafetus / babby format, despite the fact that he now fails to address any questions regarding the new teams that have propped up as the Spring dates were announced.

What instead happened was Lear gave a 48 hour ultimatum to /hm/ and /aco/ to get a thread ready and gather interest, and then cut them off short of the 40 teams count despite there being a good chance /aco/ will in fact make it, without even considering the possibility that there may be wildcards (/t/, /gif/) or reviving an autopilot with none\partial interest (/hm/ has renewed aesthetics, and at least some interest despite the disappearance of their poller - which does not seem a problem for /cm/).

Despite the fact that the people voted for more teams, and for making a megababby happen if 40 teams were interested, despite the huge support this tournament format had in Autumn, Lear decided, on his own, to stick with a format that is unpopular and that saves absolutely no time for the streamers.

## Conclusion and Signatures

In conclusion, due to the reasons listed and way more that you are all well aware of, we believe it is time for Lear to part with the role of Commissioner.

We are aware this is not the first time this discussion has come to a sticking point, and would therefore propose Shakes as the new Commissioner of the 4chan Cup, following a vote of no confidence.

Signed,

MarcoZ (talk) 18:57, 8 April 2018 (UTC)
Ordinate (talk) 19:42, 8 April 2018 (UTC)
Megabeastage (talk) 19:46, 8 April 2018 (UTC)
Sillius (talk) 19:47, 8 April 2018 (UTC)
Canes (talk) 19:53, 8 April 2018 (UTC)
Labcoat (talk) 19:57, 8 April 2018 (UTC)
ravenire (talk) 20:04, 8 April 2018 (UTC)
DescendingBear (talk) 20:09, 8 April 2018 (UTC)
Suule (talk) 20:26, 8 April 2018 (UTC)
rhs (talk) 20:26, 8 April 2018
MS (talk) 20:31, 8 April 2018 (UTC)
a useless shitter 20:31, 8 April 2018 (UTC) shit nobody cares about
TSparx (talk) 20:33, 8 April 2018 (UTC)
GMG (talk) 20:33, 8 April 2018 (UTC)
Tuvalu (talk) 20:39, 8 April 2018 (UTC)
North (talk) 20:41, 8 April 2018 (UTC)
Myuer (talk) 20:49, 8 April 2018 (UTC)
Blinky (talk) 22:21, 8 April 2018 (UTC)
Aitor Karanka !!vHwU8e1Ta/3 22:50, 8 April 2018 (UTC)
Prow (talk) 22:56, 8 April 2018 (UTC)

## Pussies that are abstaining from this motion

Kostas GRE (talk) 23:19, 8 April 2018 (UTC)

## This is fucking stupid

Signed,
MaxPiston (talk)
(´・ω・) (talk) 20:13, 8 April 2018 (UTC)
Lear is a Boris-enabling cuck and they both should be sacked but this is some of the dumbest shit I've ever seen Carmastrikes (talk) 20:21, 8 April 2018 (UTC)
Carma sums it up nicely CoIlieBro (talk) 20:25, 8 April 2018 (UTC)
I have no strong feelings one way or the other. EDIT: While there are some legitimate grievances made, I believe it's worth point out that WE'RE PLAYING MEMEBALL ON THE INTERNET. CptCourage (talk) 20:28, 8 April 2018 (UTC)
There's a tradition in the Bittenfeld family! When you praise someone you do it loudly; when you denounce someone you do it even louder! I'm only observing that tradition. Bittenfeld (talk) 20:53, 8 April 2018 (UTC)
I had 0 time to help /cm/ at all and it's like /c/ where it really isn't a board you "main", so it's a little difficult without dedicated posters for it. I support removing /cm/ but doing all this because Lear hurt your feelings or whatever is dumb and the cup shouldn't be taken this seriously. The intense shit that comes from this dumb video game is why some people can't be bothered doing it for a long period of time. RoronaBest (talk) 20:42, 8 April 2018 (UTC)
I can't believe Gimi broke that guys shins Blinky (talk) 22:19, 8 April 2018 (UTC)
no - Smugleaf (talk) 00:49, 9 April 2018 (UTC)
whoever removed my signature is a faggot - Mantis (talk) 04:14, 9 April 2018 (UTC)

## I want my own section

PM me anime ass RamenRaisin (talk) 20:33, 8 April 2018 (UTC)

## Can I have Boris back please

Niggers,
Lowroller (talk)

Ignore below me, he is a liar, Go fuck yourself Collie, lil bitch

## Fuck the above post, Boris was sacked for a reason

Chat shit get banged,
CoIlieBro (talk) 20:17, 8 April 2018 (UTC)

Ignore above me, he says mean words. I cannot condone this language on a family website.

This guy for commish > Blinky (talk) 22:22, 8 April 2018 (UTC)

## IMGAY

Hello... Sargbot. Carmastrikes (talk) 20:38, 8 April 2018 (UTC)
Hey Carma..... Long time no talk, how's it going? Sargbot (talk)
Pretty good bb, gettin good grades and shit since I quit this dupster fire, and yet for some dumb reason I wanna come back. hbu? Carmastrikes (talk) 20:40, 8 April 2018 (UTC)
Currently waiting on a new job to start, happy to be out of this 4CC nonsense tbqh. My PES days are long since over. Sargbot (talk)
Nice man I'm glad you're free of it. I hope everything works out for you, lad. Carmastrikes (talk) 20:45, 8 April 2018 (UTC)
Same to you bb, hope life is treating you well. Sargbot (talk)
I'm gay for fictional girlsDrDtroit (talk) 20:53, 8 April 2018 (UTC)
Also make me commish and i'll not only remove /cm/ but also give everyone a free Doritos Locos Taco while supplies last DrDtroit (talk) 20:56, 8 April 2018 (UTC)
But you have to buy the cinnamon twists yoruselves DrDtroit (talk) 20:56, 8 April 2018 (UTC)

## /w/ issue is completely legit

The rest is wankery. /cm/ first PoI scandal was handled correctly as he had public endorsement for the call. /cm/ second PoI scandal is borderline, and maybe even if /cm/ shouldn't play, it's not an issue warranting an impeachment. /u/ stuff is irrelevant. His opinions are wrong but he never took any action against /u/, only shittalked them on FB. Mentioning /hm/ is downright wrong because the guy who was interest died weeks ago, so /hm/ wasn't realistically in contention for revival. The 39 assessment was correct. If there's one thing that needs to change, it's signups have to be brought back so we avoid situations like this phantom megababby one again. Because of all these points I don't agree with, I can't in good faith sign the letter.

Make a new petition only saying "we want to change Lear with Shakes because we believe Shakes is more competent" and I'll gladly sign.
TWAIN (talk) 20:53, 8 April 2018 (UTC)

Lear needs to be sacked because his ethos for running the cup is creating a wash of bureaucratic nonsense that is detracting from the state of the cup as a targeted form of shitposting and autism. We don't need autistic PoIs to prevent dead teams from getting into the cup. The fans care less about what team is doing what than you idiots think. As long as a team is fun it'll have people who like to watch them play, or at least don't mind watching their own team play against them.

The cup needs to be rolled back to a state that is comprehensible and impervious to stupid bullshit drama like this and like the dumb shit that Lear keeps kicking up. I know the good old days weren't perfect but they were a hell of a lot more sane than this retardation.

Lear and Boris need to have their influence removed from the cup. This vote of no confidence is an excuse and if it works then so be it but this revolution is built on shaky ground and empty stomachs. Have a plan before you act.

Consider this my vote for the resignation of Lear and the instatement of Shakes to the position of 4cc Commissioner, even if your manifesto is fucking stupid and dances around the real fundamental issues that Lear has brought to fruition in the Cup.
Carmastrikes (talk) 21:04, 8 April 2018 (UTC)

Add to this that when f4r and/or Boris make a decision (even on dumb shit nobody will care much about), Lear doesn't have the balls to override them. What's the point of having a commissioner if he can't properly lead without the guidance of someone we already gave the vote of no confidence? This is a 4chan event, it doesn't need a complex system checks and balances like it was bloody congress. What it needs is someone up top making the little decisions, a group of 5-10 people who *help* make the bigger ones, and a mass of shitposters underneath who removes the commissioner if he proves incompetent at his job. Until this happens, the cup will suffer.

Also, cut /w/, it's not worth the drama it caused. CoIlieBro (talk) 21:19, 8 April 2018 (UTC)

I agree with what TWAIN and Carma have said. Lear has to go but I don't care too much about the mega babby or megafetus. rhs (talk) 21:08, 8 April 2018 (UTC)

Making Shakes commish changes nothing, solves nothing and fixes nothing. There will always be drama, there will always be people who start drama to fill the holes in their souls. If you want to fix the cup, start with (You). It is always (You). Fuck this and everyone involved in it 22:22, 8 April 2018 (UTC)

This section is the only one with any merit (get it lol). But yeah the majority of this "letter" is dumb and gay. Sargbot (talk) 21:26, 8 April 2018 (UTC)

Still gonna keep my signature up but what I said in “shit nobody cares about” is basically why I signed this shit. /cm/ should either get new interest or not play by the established PoI standards (or PoI standards should be eliminated), Lear is wrong and dumb about /u/ polling but all he’s actually done is talk shit on First Bait which is basically the point of First Bait and isn’t even remotely worthy of anything but a hearty laugh, and I don’t care much about babby format. Let me watch some goddamn divegrass. Everyone is a cuck. Washed up wiki autist - Please edit our wiki 21:53, 8 April 2018 (UTC)

Honestly, the fact that /merit/ discussion are in the dark make no sense in a 4chan cup. Shit has to be out in the open in order for shitposting and trolling to either strengthen or weaken the argument involved (If the idea is actually good, then shitposts look dumb and thus reinforce the idea. If the idea is bad, shitposts look smart and thus degrades the idea). This is how 4chan operates. The fact that both /merit/ discussions take place in the dark AND Lear on this last outburst blamed all his actions on being ones that /merit/ voted on means that people on the outside have literally no idea what exactly is happening, which can’t be good. It blocks the shitposting needed to really determine if the action is good until after the action has already been made. This coupled with the fact that the decision took so long to become finalized and then when finalized is unable to be modified in any way is just plain dumb.
Figure out a way to make decisions that allows shitposting to have its fun in the sun as well. The /w/ shit was an eye opener for me but this /cm/ and /t/ thing just go to show that decisions seem to be made by the seat of /merit/‘s and/or Lear’s pants, which shouldn’t be the role of the commissioner or the commissioning body. CaptPlanet (talk) 13:07, 9 April 2018 (UTC)

I wholeheartedly agree with CaptPlanet. I can kinda understand why it was done like this back in the Skype days, but now that we're using Discord I see no reason to not make a separate /merit/ channel where everybody has viewing rights but only /merit/ members can post. I feel like it'd solve a lot of issues to just know what's going on. Sillius (talk) 15:42, 9 April 2018 (UTC)

## VGL Council replaces /merit/ and Lear, there is no formal commissioner

Our cup is based and has 0% of the drama 4CC has on the daily. The reason for this could be 1) it's not the main cup 2) it gets a quarter of 4CC attendance and 3) It's actually fun and lax?

Most of the best memories I have of the cup is from 2012/13 and a brief period in 17 where I believe things were at their best PURELY because the cup was not an event that had countless namedropping, tons of witch hunting, and a STAFF (or was it just GB, idr if 4CCC was a legit group or not) of people making decisions that focused on one thing and that was keeping the cup FUN and the both the regular and casuals happy. Bias is something that cannot be prevented, there is no such thing as an unbiased person but if there is a GROUP of people and no HEAD PERSON named as the leader it can be organized and taken care of easier. What I do in VGL is I take up every single case and discussion to the council and discuss how to handle it before me or literally anyone else in there goes public with the decision. I know >VGL and everything but I care a lot for the managers, the viewers, and the shitposters who are both heavily involved and not involved at all. What started as a silly side tournament has grown into something I want to properly maintain and have it continue for many years.

Breaking off from that tangent and getting back to the point, if we discontinue the role of commissioner and leave the hands of 4CC in the hands of trusted people and contributors, we can prevent something like this "bias" shit happening again. But what I'm really trying to say is replace /merit/ with VGLC :)

With love and kisses, (´・ω・) (talk) 21:18, 8 April 2018 (UTC)

Meming aside, removing the commissioner role has a lot of merit. rhs (talk) 21:20, 8 April 2018 (UTC)

haha "merit" RamenRaisin (talk) 21:24, 8 April 2018 (UTC)

hahahaha yes /ag/ wins again we RUN this shit fellas /4ccg/ on suicide watch Cyclohexane (talk) 21:25, 8 April 2018 (UTC)

/ag/ IS LAUGHING AT US AGAIN WTF BROS THIS ISN'T FAIR

Having a group of people make the decisions sounds like a more plausible idea than just having a single guy have the final say. Some if not most decisions by Lear were handled poorly because of sheer bias which could be avoided by introducing a system like the one VGL uses. I am not sure about making Shakes sole commissioner like suggested. Not because I don't trust him, but because the guy is already loaded with aesthetic work for both 4cc and VGL Resolink (talk) 21:38, 8 April 2018 (UTC)

absolutely co-signed Magicblue (talk) 22:24, 8 April 2018 (UTC)

yes this --Autocrat (talk) 23:02, 8 April 2018 (UTC)

yo can i have a fuckin uhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh KinseyTypeF (talk) 03:24, 9 April 2018 (UTC)

imagine deleting both my signatures kys my mans - Mantis (talk) 04:15, 9 April 2018 (UTC)

/4ccg/ IN THE VGL WHEN

## Appendices

### Appendix 1

[2017-08-23 01:36:21] Descending Bear: similiarly, if we wouldn't have a single trustworthy person on board to verify this poll, I'd still advocate for asking /cm/ fans to run it again (not whole thread with POI, just the poll, this one supervised by one of us)
[2017-08-23 01:37:18] Descending Bear: perhaps we'd reach the solution of seeking help among actual /cm/ fans on our own, perhaps we could achieve it by having a discussion with managers
[2017-08-23 01:38:34] Descending Bear: however, throwing half of us to the ptchforks without letting us know before we've reached any kind of agreement is disgusting, and defending that it was a right thing to do is equally disgusting
[2017-08-23 01:39:15] f4r !HanakoDlmg: the main schism seemed to be around running another poll or not
[2017-08-23 01:39:34] Descending Bear: I don;t particularily care about "reputation", but being thrown under the bus for things I haven't said or done is not what any of us is here for
[2017-08-23 01:39:34] King Lear: Running a second poll is voiding the first one.
[2017-08-23 01:39:56] Descending Bear: yes, and that would be required if we wouldn't find any proof of validity
[2017-08-23 01:39:57] King Lear: Bear you said that /cm/ should have their POI scrapped and another poll ran.
[2017-08-23 01:40:13] King Lear: Running a second poll is scrapping the POI.
[2017-08-23 01:40:49] Descending Bear: no, telling them to start a new thread would be scrapping POI
[2017-08-23 01:41:15] Descending Bear: or demanding that existence of this poll means nothing at all and /cm/ fans do not exist
[2017-08-23 01:41:56] King Lear: >hey you know that poll you voted in well it didn't count try again
I call that scrapping the POI.
[2017-08-23 01:42:57] Descending Bear: this is only according to your very specific definition of POI
[2017-08-23 01:43:35] Descending Bear: In case of small and slow boards, I often encourage manager candidates to ask for suggestions in thread rather than running the poll
[2017-08-23 01:44:08] Descending Bear: what I men is, poll is not technically required if there was discussion about players, music and whatnot, and manager/autopilot follows those advices
[2017-08-23 01:45:30] Descending Bear: while DF is perfectly capable of pretending to be several people, it;s pretty obvious that even if he would, thread like that still gathers some interests of /cm/ anons who stumbled upon it and might have posted in it
[2017-08-23 01:46:28] Descending Bear: I've never called for throwing /cm back to step zero, only to have a poll that is not run by the most banned person in this Cup
[2017-08-23 01:48:07] King Lear: Saying the poll didn't count is scrapping the POI.
[2017-08-23 01:48:55] Descending Bear: gaining proper board interest is actually pretty complex process that has several steps:
- attracting attention of board denizens;
- explaining to them on what the Cup is;
- explaining to them what does manager expect from them and waiting for their feedback;
- making sure that board stays interested and informed once the team plays in actual Cup
[2017-08-23 01:49:00] King Lear: That isn't even mentioning how dumb a second poll is as an idea.
[2017-08-23 01:49:30] King Lear: - attracting attention of board denizens;
- explaining to them on what the Cup is;
- explaining to them what does manager expect from them and waiting for their feedback;
- making sure that board stays interested and informed once the team plays in actual Cup
The poll did all but the last one which it could not have.
[2017-08-23 01:49:59] Descending Bear: if you're calling invalidating just one of those steps as being equal with scrapping POI, you really have no idea on what are you talking about
[2017-08-23 01:50:27] King Lear: Want me to ask the audience on this one? you're telling the fans their vote didn't count, that's scrapping the POI.
[2017-08-23 01:51:03] Descending Bear: because even when poll is redone, the fact is, some of /cm anons already know what the Cup is and might be curious enough to stick around, and that's a lot more than having nothing at all
[2017-08-23 01:51:19] King Lear: So you admit a second poll would drive people away.
[2017-08-23 01:51:44] Descending Bear: and now I have no idea what are you talking about
[2017-08-23 01:51:59] King Lear: Alright so what would a second poll do that the first one didn't?
[2017-08-23 01:52:11] Descending Bear: no, it wouldn't if we are not scaring /cm/ fans with drama, and we wouldn't have to
[2017-08-23 01:52:55] King Lear: No matter the approach if you tell people for any reason their vote did not count they will not be happy.
[2017-08-23 01:53:12] King Lear: And if I were one of those people I would feel that I had wasted my time for no reason.
[2017-08-23 01:53:37] Descending Bear: you don't need to give a valid reason, something along the lines of "oops, this formula did not gave us enquivocal results / we need some tiebreakers" or whatever you think of
[2017-08-23 01:53:57] King Lear: No matter what you say, if people have to vote a second time they'll be unhappy.
[2017-08-23 01:54:09] Descending Bear: yeah, spending 2 minutes on voting is such a chore, it can be done only once a year to not overextert oneself
[2017-08-23 01:54:10] King Lear: Especially if the poll is the same.
[2017-08-23 01:54:38] Descending Bear: then you change things in poll formula to make it look and work differently, there are endless possibilities
[2017-08-23 01:54:55] Descending Bear: more candidates in roster suggestions in new poll, basically anything
[2017-08-23 01:55:21] King Lear: So if we change the poll people who have their choices affected now feel as though they are being told to fuck off.
[2017-08-23 01:55:36] Descending Bear: this is null discussion though as we've agreed to accept /cm/ poll as it is, at leat for this one season
[2017-08-23 01:56:23] King Lear: Yup because it turns out that thinking the POI should be voided and a second poll ran is a bit of a minority opinion at large.
[2017-08-23 01:57:25] Descending Bear: and about your idea of bringing it to the public: sure tell them in all details how evil bear is plotting to kill /cm/ again. Nothing like a good walk of shame to bring fellow member back to order, isn't it
[2017-08-23 01:58:20] Descending Bear: I can't believe I really tried to maintain integrity of /merit/ by standing your side and defending you when you were the minority for the stunt you wanted to pull off with /w/
[2017-08-23 01:58:50] King Lear: Yup I said in public you wanted the POI scrapped.
[2017-08-23 01:59:24] Descending Bear: if you want to invoke the rule of majority whenever you need and ignore it when it does not suit your agenda, go ahead

### Appendix 2

[6:58 PM] Lear: @Free my nigga megababby I told you yesterday that /cm/ have new poi, not sure why you are saying today they dont.
[6:59 PM] Free my nigga megababby: I said something specific: >without re-polling
[7:00 PM] Free my nigga megababby: Autumn poll, Spring cup, doesn't look like a cup cycle to me even though I guess that rule has been wiz'd away right about now.
[7:00 PM] Incoming: I mean /cm/'s current roster is bretty good aethstically
[7:00 PM] Free my nigga megababby: Without even getting into the legitimacy of that thread
[7:03 PM] Lear: That's pretty narrow if you think the p in poi can only stand for poll. If there is a thread that shows a team clearly wanting to play rejecting it because they were being interested and discussing the Cup in the wrong way would be stupid.
[7:05 PM] Free my nigga megababby: So you're saying that it is technically possible to keep a team unupdated for multiple cup cycles and potentially years without ever even updating the roster as long as they have a matchday thread of completely anonymous supporters
[7:05 PM] Free my nigga megababby: With one of the commentators announcing your thread on stream and still being legitimate
[7:08 PM] Free my nigga megababby: It's in my history so I must have skimmed through it, the first post is literally "raid incoming" though, had an hearthy laugh
[7:11 PM] Lear: The thread went on for a while after it got brought up and had actual discussion in it so I feel it is better to give them the benefit of the doubt this once. As for the roster thing if the people on the board are happy with the roster and there is interest in the team then telling them their interest wasnt correct is being petty and shutting out a team with interest.
[7:15 PM] Free my nigga megababby: So the cup cycle thing hasn't been written out after all and you're only giving them a pass for a healthy thread, despite the fact that every other autopilot and post-cull team past and present had to get a reputable, non banned tripfag to drum up interest for them to return to the cup, and despite the fact that the thread was leaked in an incredibly visible location and that it literally starts with two 4ccg shitposts
[7:19 PM] Lear: >reputable, non banned tripfag
Only thing we care about is not banned. If we didnt let a team in because the person who made the thread wasnt a top lad that'd be fucked.

Yes their thread was leaked and we are going to be more harsh on that in the future but dont act like the thread has nothing but people shouting about raids.

## Counterpoints

Didn't free /t/

Not yet, be a little patient

(USER WAS BANNED FOR THIS POST)

## benis

benis PWJP (talk) 20:49, 8 April 2018 (UTC)
benis Metagross01 (talk) 21:14, 8 April 2018 (UTC)
benis Polybius (talk) 21:19, 8 April 2018 (UTC)
benis Sargbot (talk) 21:26, 8 April 2018 (UTC)
benis Kostas GRE (talk) 21:29, 8 April 2018 (UTC)
benis Foojile - Is it time, brothers? 21:34, 8 April 2018 (UTC)
benis CptCourage (talk) 22:26, 8 April 2018 (UTC)
bepis Labcoat (talk) 01:11, 9 April 2018 (UTC)
benis Equinox (talk) 01:12, 9 April 2018 (UTC)
benis Clingingmars (talk) 01:14, 9 April 2018 (UTC)
benis John Hayabusa (talk)
benis KinseyTypeF (talk) 09:29, 9 April 2018 (UTC)
benis CoIlieBro (talk) 10:58, 9 April 2018 (UTC)

## an open letter to my ass

fisting is 300 bucks Cyclohexane (talk) 21:13, 8 April 2018 (UTC)

## My little hidey-hole

I swear to god if any of you FUCKS copy and paste this you will be is serious trouble Kostas GRE (talk) 21:05, 8 April 2018 (UTC)

"I LOVE SUSHI!" exclaimed the woman in the thick-rimmed glasses. "Ah, excellent," Kobayashi thought contentedly to himself, "they are enjoying themselves." "I love Japan, period" said the middle-aged man in the blue shirt, slight southern drawl lending a down-home earthiness to his earnest proclamation. "Oh my, it is such a joy to have such enthusiastic customers!" Kobayashi said to himself, beaming with pride at the delight he had brought to his customers. It was an idyllic day in Kobayashi's small sushi shop. But, then things took a turn for the worst. "J-ROCK!" screeched a greasy-haired delinquent, quite obviously high on something. "Oh my, someone should be watching over that poor child," Kobayashi thought to himself. But, before he could finish that thought, a rotund man burst forth from the masses, the make-up on his face still smeared across his fleshy visage. "GIRUGAMESH!" the horrifying painted man exclaims, stabbing the air vehemtly with two massive, pudgy digits. "What has begun here is something terrible," Kobayashi thinks to himself, rooted in place by equal parts fear, and morbid fascination. "I LOVE ANIME!" shrieks a curiously toupee'd customer, the disparity of voice and adornment calling into question the beast's gender. "AND MANGA" yells the man-lady's back-quatto, the horrifying extra upper torso protruding from the hermaphrodite's back, malign intent dancing across his/her eyes. Kobayashi is speechless at the spectacle unfolding before him. "AND GAYMEN!" an infernal scarecrow man drunkenly spews forth, every diabolical syllable dripping from his tongue an affront to sanity and dignity. "Uh...DDR?," says a man quite plainly. "Finally, a respite from this madness," Kobayashi thought as he heaved a breathless sigh of relief. But what he had seen so far could never prepare him for what came next. "SMILE D.K." squealed the man's bloated pig-wife, barely managing to stay balanced atop her chair. As these things happened, a realization dawned on poor, poor Kobayashi. "These people, these DEMONS, have taken all I know and love and made it wrong, corrupted it. I can not, no, I will not sit idly by as these creatures from beyond the veil wreak havoc in my shop!" "HEYYYYYY!" Kobayashi growls, brandishing his knife like a modern day warrior. "SAKURA-CON HE IKIMAAAAAAAAAASU" he bellows, the traditional war-cry of his family. As Kobayashi leapt over the table, the gathered masses began morphing, face tearing asunder to reveal rows upon rows of sharp teeth, as new musculature rippled forth from beneath their clothes. Many dropped to all fours, revealing their true bestial nature, snarling and snapping their jaws at Kobayashi. Like a true warrior, however, he dove fearlessly into the throes of battle, slicing sinew and bone alike with a precision afforded him by his years of chef training. He laughed maniacally as bucket upon bucket of blood was spilled, the organs and flesh of his former patrons spewing forth like water down a hill. He and his restaurant alike were soon strewn with every type of viscera, and he gave an animalistic howl to the still-rising moon. Kobayashi goose-stepped over the knee-high pile of cadavers, and, having finally exited the restaurant, he wiped the blood clean from his cleaver and strode off into the horizon. He knew that he had honored his ancestors with this true act of bravery, and helped to rid the world of a grave evil indeed.

(USER WAS BANNED FOR THIS POST)

░░░████▌█████▌█░████████▐▀██▀
░▄█████░█████▌░█░▀██████▌█▄▄▀▄
░▌███▌█░▐███▌▌░░▄▄░▌█▌███▐███░▀
▐░▐██░░▄▄▐▀█░░░▐▄█▀▌█▐███▐█
░░███░▌▄█▌░░▀░░▀██░░▀██████
░░░▀█▌▀██▀░▄░░░░░░░░░███▐███
░░░░██▌░░░░░░░░░░░░░▐███████
░░░░███░░░░░▀█▀░░░░░▐██▐███▀▌
░░░░▌█▌█▄░░░░░░░░░▄▄████▀░▀
░░░░░░█▀██▄▄▄░▄▄▀▀▒█▀█░▀

## This couldn't have waited until tomorrow?

Thanks for RUINING my Sunday night. CptCourage (talk) 21:10, 8 April 2018 (UTC)

(USER WAS BANNED FOR THIS POST)

## It's Fucking Memeball

Why are you all fucking autistic? Vaughan (talk) 22:49, 8 April 2018 (UTC)

## fuk dag

see section title Dag (talk) 00:50, 9 April 2018 (UTC)

why did you delete my text QD (talk) 01:19, 9 April 2018 (UTC)

## Chris Benoit Killed His Family

It's always been a fantasy of mine to be a sex slave for 2 bears, male and female, pleasing the male when she's tired, and vice versa. Slowly sliding my lips up and down his thick shaft, tasting his pre-cum on my tongue. Once he's had enough of that, he rolls over onto his back, lifting me up as though I weighed nothing. Gently placing me on his cock, I guide him in, feeling him stretch me wide open. I moan with pleasure, feeling him fill me up. He growls softly, I feel it rumble deep in his chest, vibrating all the way down his body and through mine. He continues to lift me up and then pull me down. He's doing all the work for me, it feels so good, the warmth of the fur, his paws either side of my waist. He is in total control, I'm just nothing compared to his vast size and strength, but I have total trust in him, I know he won't hurt me. I feel the pace quicken, almost imperceptibly. I slowly stroke myself, feeling myself nearing the point of no return coming closer with every stroke. I can hear the growl getting louder now; he speeds up even more, forcing me further and further down onto his thick cock. If it wasn't for the fact I my body is releasing so many endorphines, I would probably be screaming in agony. Except I am panting and whining, just like a bitch, begging her mate to fill her up. His claws dig in deeper, the pain, its excsquisite. It sends me over the edge. My head goes back, I let out a short grunt, I feel my cock explode, covering his chest fur in my seed. I keep stroking, it looks as though I'm trying to rip my cock out. I let out another grunt, another torrent flows forth, then another and another. A drop lands on the beasts muzzle. He seems confused for a moment. That's what I think. He digs his paws in even harder now and slams me onto his cock, I feel his grumble turn into a roar. He's cumming, oh my god. I can feel in, filling me up. It's undescribable. He's mating with me, he's claimed me. I feel him slow, his cock still throbbing within me, it seems as though there's no more room for his cum. It's dripping out of me, onto his fur. I reach down, and then bring my hand up, tasting him. It's more than I ever expected. It's heaven. /wooo/ (talk) Then, Now, Forever (UTC)

## Not Shakes

Shakes is complicit in the protecting of Dragonfag and hiding him in Aesco 2.0, and creating a independent Aesco from the 4CC purely to protect him. While you could argue this is warranted for Shakes to protect one of his better workers, having him as Commisionner would verify Dragonfag by proxy Which, to be reminded, he hasnt recovered from his sockpuppet ways, trying to take control of /cm/ by proxy setting up their revival polls and was close to Johnny who was nearly given the job of making Autopilot Exports. He would have been in control of multiple teams again.

Anyone but Shakes 6letters (talk)


text:
Share

# When X^3 + 2x ^2– Kx + 4 Is Divided by X – 2, the Remainder is K. Find the Value of Constant K. - Mathematics

Course

#### Question

When x^3 + 2x ^2– kx + 4 is divided by x – 2, the remainder is k. Find the value of constant  k.

#### Solution

Left f(x)=x^3+2x^2-kx+4

x-2=0⇒x=2

on dividing f (x) by x-2,, it leaves a remainder K.

∴ f(2)=k

(2)^3+2(2)^2-k(2)+4=k

8+8-2k+4=k

20=3k

k=20/3=6(2)/3

Is there an error in this question or solution?

#### APPEARS IN

Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 8: Remainder and Factor Theorems
Exercise 8(A) | Q: 9 | Page no. 108

#### Video TutorialsVIEW ALL [2]

Solution When X^3 + 2x ^2– Kx + 4 Is Divided by X – 2, the Remainder is K. Find the Value of Constant K. Concept: Remainder Theorem.
S


text:
# When 1.3 g of KClO3 was added to 151.1 g of water in a calorimeter, the  temperature...

###### Question:

When 1.3 g of KClO3 was added to 151.1 g of water in a calorimeter, the  temperature dropped by 0.588 °C. The heat capacity of H2O is 4.184 J/g°C. Assume the  specific heat of the solution equals that of pure H2O and that the calorimeter neither  absorbs nor leaks heat. What is the molar heat of solution of solid potassium chlorate? Give the answer in kJ.

#### Similar Solved Questions

##### "The combination is the seventh, ninth, and eleventh numbers in a sequence that begins 1,1,2,3,5,8,13, and so forth" What is the combination
"The combination is the seventh, ninth, and eleventh numbers in a sequence that begins 1,1,2,3,5,8,13, and so forth" What is the combination? I have a problem with this can you help?...
##### Adjusting Entries Written Homework Journalize the necessary adjusting entry for each of the following independent situations:...
Adjusting Entries Written Homework Journalize the necessary adjusting entry for each of the following independent situations: 1. The supplies account balance on September 1, 2020 is 53,975. The supplies on hand on September 30" are $1,050 2. On January 1, 2020 the company paid$3,600 for an annu...
##### Chrum BIO 139 Identify the following Structures SYSTEMIC CIRCULATION PULMONARY CIRCULATION
chrum BIO 139 Identify the following Structures SYSTEMIC CIRCULATION PULMONARY CIRCULATION...
##### In the vector space of polynomials of degree or less (Pz) determine if the set of vectors 8 = {2 +t- 3t2 Bt3 , 1 +t +t2 + 5t*,3 4t2 7t3}Is linearly independentFind vector in Pz that is not in the span of 5.
In the vector space of polynomials of degree or less (Pz) determine if the set of vectors 8 = {2 +t- 3t2 Bt3 , 1 +t +t2 + 5t*,3 4t2 7t3} Is linearly independent Find vector in Pz that is not in the span of 5....
##### Are my feet are killing me is a alliteration, personification , or hyperbole
are my feet are killing me is a alliteration, personification , or hyperbole?...
##### Draw all of the isomers there are for [Ru(en)2Cl2]+ and name each.
Draw all of the isomers there are for [Ru(en)2Cl2]+ and name each....
##### Do you consider it ethical to violate a DNR?
do you consider it ethical to violate a DNR?...
##### Question 38 (2 points) A steam turbine receives 10 kg/s of superheated steam at 120 bar...
Question 38 (2 points) A steam turbine receives 10 kg/s of superheated steam at 120 bar and 600°C. The steam expands adiabatically through the turbine and exits at a pressure of 0.2 bar and a quality of 90%. The steam inlet velocity is 200 m/s and the exit velocity is 50 m/s. Determine the power...
##### If you are calculating surface area of a right circular cone topped with a hemisphere
If you are calculating surface area of a right circular cone topped with a hemisphere. the radius is 4 cm and the rt angle is 8 cm...what is the lateral surface area. Is it 8.94 or is it 9? Explain answer please. Thanks...
##### Part ! Molar_Enthalpy of Reaction of Magnesium with Hydrochloric Acid Frst Run Second Run Timeminutes Temp _ 01"C Time minutes Temp + 0.L % 245 23.2 24.5 23.2 24.5 23,.224.5 24.5 24.51/223.223.22 1/223.2 23.224.5 24.53 1/223.2 23.224.524.54 1/223.2Add Mg_swirl to mix: Note the time of addition_ 30.524.531.8 32.55 1/228.429.133.06 1/230.130.133.11430.0 29.9 29.7.33.133.18 1/2
Part ! Molar_Enthalpy of Reaction of Magnesium with Hydrochloric Acid Frst Run Second Run Timeminutes Temp _ 01"C Time minutes Temp + 0.L % 245 23.2 24.5 23.2 24.5 23,.2 24.5 24.5 24.5 1/2 23.2 23.2 2 1/2 23.2 23.2 24.5 24.5 3 1/2 23.2 23.2 24.5 24.5 4 1/2 23.2 Add Mg_swirl to mix: Note the tim...
##### When P(x) = ax^3 +bx^2 + cx + d is divided by x+2, the remainder is -5. Find a possible set of the constants, a, b, c and d ?
When P(x) = ax^3 +bx^2 + cx + d is divided by x+2, the remainder is -5. Find a possible set of the constants, a, b, c and d ?...
##### Find the particular solution of the following differential equation using the indeterminate coefficients method. Also find...
Find the particular solution of the following differential equation using the indeterminate coefficients method. Also find the general solution....
##### ProblemFiud the domain of f 0 g of the following functions:f(r) =and g(s)f(I)and g(T)ProblemDetenmine if g(1) is the inverse of f(c)f(t) J T and g(=)=f(c) = +4and g(r) =
Problem Fiud the domain of f 0 g of the following functions: f(r) = and g(s) f(I) and g(T) Problem Detenmine if g(1) is the inverse of f(c) f(t) J T and g(=)= f(c) = +4and g(r) =...
##### [-/0,66 Polnts]DETAILSCRAUDQL3 8.4.022MY NOTESASK YOUR TEAEHnell (own uluckHnenJo ponnd memben from (our districLs: North, South;Wcst; Tho populatlons cach district are shown bulow;DlntrictPopulationFgnanSouthWtHnd the ditribution board mcuberg ullng Adams  method nlatEci WOnnO KnambrcnNatbnSouthEestMontSubmlt Asstgnment Suve Asilcnmient Progress
[-/0,66 Polnts] DETAILS CRAUDQL3 8.4.022 MY NOTES ASK YOUR TEAE Hnell (own uluck Hnen Jo ponnd memben from (our districLs: North, South; Wcst; Tho populatlons cach district are shown bulow; Dlntrict Population Fgnan South Wt Hnd the ditribution board mcuberg ullng Adams  method nlatEci WOnnO Knambr...
##### The voltage in the lines that carry electric power t0 homes is typicallv 2000 V What is the required ratio of the loops in the primary and secondary coils of the trans former t0 drop the voltage to 120 V?
The voltage in the lines that carry electric power t0 homes is typicallv 2000 V What is the required ratio of the loops in the primary and secondary coils of the trans former t0 drop the voltage to 120 V?...
##### Q10. (10 points) Let f(x)=x -312 _ +1-3,4] Find absolute maximum and minimum values of the function within the interval. b) Find all relative extrema, points of inflection; intercepts, concavity Sketch the graph label intercepts
Q10. (10 points) Let f(x)=x -312 _ +1-3,4] Find absolute maximum and minimum values of the function within the interval. b) Find all relative extrema, points of inflection; intercepts, concavity Sketch the graph label intercepts...
##### 1 How would you characterize the competitive strategy of high-end department store chain such as Nordstrom? What are the key customer needs that Nordstrom aims t0 fill? 2. Explain the major difference between demand uncertainty and implied demand uncertainty using the example of the iPhone 6 Plus_ 3. What would be the impact of increasing product variety on implied demand uncertainty in the case of a convenience store like 7-1? Is it correct to say that the implied demand uncertainty will correl
1 How would you characterize the competitive strategy of high-end department store chain such as Nordstrom? What are the key customer needs that Nordstrom aims t0 fill? 2. Explain the major difference between demand uncertainty and implied demand uncertainty using the example of the iPhone 6 Plus_ 3...
##### Suppose _ that your favorite fast food chain is giving away coupon with every purchase of a meal. Twenty percent of the coupons entitle you to free hamburger, and the rest of them say "better luck next time_ Ten of you order lunch at this restaurant.What is the probability that exactly two of you win free hamburger? (use binomial forula and show your complete work)What is the probability that fewer than two of yOu win free hamburger? (you may use table or calculator)
Suppose _ that your favorite fast food chain is giving away coupon with every purchase of a meal. Twenty percent of the coupons entitle you to free hamburger, and the rest of them say "better luck next time_ Ten of you order lunch at this restaurant. What is the probability that exactly two of ...
##### 71 Buntel  Cacl} 4,Ac0s Conslder the (cloring Integral [37* graphing uellity Orapie unteorand:1 A Mmntai Jraph Derermini whether the Jelinite entegral Doslve nejuot ? D0 ICrc Dosiuva ncaativeNeed Help?penhLarcalciKOnaipJafinite Inteonaegebralc Tuncionaraonina utiltVerily Vour resultEvaluele(-Jv +Need Help?Studen Asranuent-Rosponser lastadap-20610643
71 Buntel  Cacl} 4,Ac0s Conslder the (cloring Integral [37* graphing uellity Orapie unteorand: 1 A Mmntai Jraph Derermini whether the Jelinite entegral Doslve nejuot ? D0 ICrc Dosiuva ncaative Need Help? penhLarcalci KOnaip Jafinite Inteona egebralc Tuncion araonina utilt Verily Vour result Evaluel...
##### One of two alternatives will be selected to reduce flood damage in a rural community in...
One of two alternatives will be selected to reduce flood damage in a rural community in central Arizona. The estimates associated with each alternative are available. Use B/C analysis at a discount rate of 7% per year over a 20 year study period to determine which alternative should be selected. For...
##### Big Trail Running Company has started to produce running apparel in addition to the trail running...
Big Trail Running Company has started to produce running apparel in addition to the trail running shoes that they have manufactured for years. They fool that a department overhead rato would best reflect their overall manufacturing overhead usage. Based on research the following information was gath...
##### Question 19 (2 points) boy with X-Linked Agamimnaglobulineriawould not bc atopicwould have many extracellular bacterial infectionswould not bo allergic to penicillinandall of thc abovc
Question 19 (2 points) boy with X-Linked Agamimnaglobulineria would not bc atopic would have many extracellular bacterial infections would not bo allergic to penicillin and all of thc abovc...
##### "hjc PtCiInoat cremicaly slmllar to the element Indicated the Ietter R in the following periodic table?Tticeuniu "Ftne]aeeetteauaulaea
"hjc PtCi Inoat cremicaly slmllar to the element Indicated the Ietter R in the following periodic table? Tticeuniu " Ftne]aeeetteauau laea...
##### 10. A boat heads cross-stream at a right angle to the river flow with velocity 10...
10. A boat heads cross-stream at a right angle to the river flow with velocity 10 miles/hour. The river flow is 7 km/hour. Find speed of the boat is standing water...
##### Theorem 3.3 Let A be an n X n matrix, with determinant |A/ , and let c be a scalar: (1) If R1 is the Type (I) row operation (i) 2 c (i) , then |R1(A) = cAI:
Theorem 3.3 Let A be an n X n matrix, with determinant |A/ , and let c be a scalar: (1) If R1 is the Type (I) row operation (i) 2 c (i) , then |R1(A) = cAI:...
##### 7. Find all critical points of the following function. f(x) = 5x3 – x2 – 3x...
7. Find all critical points of the following function. f(x) = 5x3 – x2 – 3x +2 a) x = -1,3 b) x = 2,3 c) x= -2,2 d) None of the above...
##### What is the difference between solubility and miscibility?
What is the difference between solubility and miscibility?...
##### C) (5 points) Using the values for the mean and the variance of the total number of deaths in each country (see output above) assume that; by the end of the pandemic, the number of deaths in each country will be 10,000 less than double the amount on 8/31/20 (i.e_ for the US It would be 2x183,069 - 10000 356,138.) What would the mean and variance of number of deaths be under these assumptions?
c) (5 points) Using the values for the mean and the variance of the total number of deaths in each country (see output above) assume that; by the end of the pandemic, the number of deaths in each country will be 10,000 less than double the amount on 8/31/20 (i.e_ for the US It would be 2x183,069 - 1...
##### According to the health behavior model, which statement exemplifies a cue to action? Question 1 options:...
According to the health behavior model, which statement exemplifies a cue to action? Question 1 options: a) The personal realization that having unprotected sex puts an individual at increased risk for contracting a sexually transmitted disease. b) A public service announcemen...
##### 10 ml of propionic acid 0.1 M CHBCHZCOOH pKa = 4.88 are titrated with sodium hydroxide Caustic 0.1 M (NaOH) Which one is correct?Before titration the pH is 2.41 and the chromocresol green pKa 4.66 is a Colored indicators suitable for determining the end point of titrationBefore the titration the pH is 2.60 and the phenol red (pKa 7.81) and is a Colored indicators suitable for determining the end point of titrationBefore titration the pH is 2.94 and the chromocresol green pKa 4.66 is a Colored in
10 ml of propionic acid 0.1 M CHBCHZCOOH pKa = 4.88 are titrated with sodium hydroxide Caustic 0.1 M (NaOH) Which one is correct? Before titration the pH is 2.41 and the chromocresol green pKa 4.66 is a Colored indicators suitable for determining the end point of titration Before the titration the p...
##### Question 19The following information are given for pure substance Z: Normal boiling point is 115 % Temperature at the triple point is 10 " Solid Z is denser than liquid Z at the melting point: Critical point is at 210 'â‚¬ and 46 atm. Sublimation can take place at pressures below 0.040 atm.Which of the following statements is false for Z?Your answer:Normal melting point of Z is higher than 10 "C. At least 46 atm pressure must be applied to liquefy Z at 211 %â‚¬ Boiling point of Z
Question 19 The following information are given for pure substance Z: Normal boiling point is 115 % Temperature at the triple point is 10 " Solid Z is denser than liquid Z at the melting point: Critical point is at 210 'â‚¬ and 46 atm. Sublimation can take place at pressures below 0.04...
##### WXX 1 ~1 M  ~E [ 1 ; L 1 1 ; 1 5 5 5 5 2 j
WXX 1 ~1 M  ~E [ 1 ; L 1 1 ; 1 5 5 5 5 2 j...
##### 17.9 A six-station automatic assembly line runs 000 hrlyr and has an idea cycle time of 10 sec. Downtime occurs for two reasons First; mechanical and electrical failures cause line stops that occur with a frequency of once per 120 cycles. Average downtime for these causes is 3.0 min. Second, defective components also result in downtime. The fraction defect rate of each of the six components added t0 the base pant . at the six stations is 0%, and the probability that defective component will caus
17.9 A six-station automatic assembly line runs 000 hrlyr and has an idea cycle time of 10 sec. Downtime occurs for two reasons First; mechanical and electrical failures cause line stops that occur with a frequency of once per 120 cycles. Average downtime for these causes is 3.0 min. Second, defecti...
##### You are a manager in charge of training recently-hired audit associates. One of the associates, Elle,...
You are a manager in charge of training recently-hired audit associates. One of the associates, Elle, asks you to explain how the knowledge of a client’s business and industry affects the auditor’s assessment of risk. You decide to use AT LEAST two of the following companies to illustrat...


text:
1. Oct 15, 2008

raghav

1. The problem statement, all variables and given/known data
In case of Cavity Radiation(Blackbody radiation) let $$\rho_{T}(\nu)d\nu$$ denote the energy density of radiation having frequency in the interval $$\nu$$ and $$\nu + d\nu$$.
Then we need to show that $$\frac{\int_{0}^{\lambda_{max}} \rho_{T}(\nu)d\nu}{\int_{0}^{\infty} \rho_{T}(\nu)d\nu} \approx \frac{1}{4}$$
where $$\lambda_{max}$$ is the wavelength at which the radiation is most intense.

2. Relevant equations
The obvious rela\evant equation is
$$\rho_{T}(\nu)d\nu = \frac{8\pi h\nu^{3}}{c^{3}}\cdot \frac{d\nu}{e^{\frac{h\nu}{kT}}-1}$$ . But the problem is the integration part. Can some one please help me with that?

3. The attempt at a solution

2. Oct 15, 2008

BerryBoy

OK, so:

$$\int \nu ^3 \cdot (e^{\frac{h\nu}{k_b T}}-1)^{-1} \cdot \delta \nu$$

Is the equation you need to solve, so you can use:

$$\int A \delta B = AB - \int B \delta A$$

(from the differentiation product rule). There's a start. Let me know if it helped.

Sam

3. Oct 15, 2008

BerryBoy

Oops, and you'll probably need this standard integral:

$$\int_0^{\infty} \frac{x^3}{e^x -1}\delta x = \frac{\pi^4}{15}$$

Sam

4. Oct 15, 2008

raghav

Yes i could evaluate the denominator using the standard integral u have mentioned, however the Numerator is creating trouble. I have also tried a parts argument, doesnt seem to be taking me any where

5. Oct 16, 2008

BerryBoy

I can't do this without some assumptions, have you stated the WHOLE question from the start?

Sam

6. Oct 16, 2008

raghav

Yes I have indeed given all the necessary details the problem demands. Essentially my doubt boils down to evaluating the integral
$$\int_{0}^{a} \frac{t^{3}}{e^{t}-1}dt$$ ; $$a$$ being some constant.


text:
# 2017 PSLE Math Question

Answer: 10 (Yes!) but why ?

…(see explanation here )

# UK Textbooks à la Chinese / Singapore Math Style

[Original Financial Times Article] Google: UK maths books fail DfE test

$\boxed {\text {Ideal Math = (Chinese + English) * French }}$

UK, USA, France are copying Chinese Math (from which the “Singapore Modeling Math” derived) in Primary schools, this proves my above-mentioned “Ideal Math” formula is correct. The 2 Asian countries were top in 2015 PISA Math Test for 15-year-old students, while UK was ranked 27th.

It remains to see if China / Singapore reciprocate the French Math theoretical foundation rigor in High Schools (Junior Colleges) and in the first 2 years of undergraduates for STEM (Science, Technology, Engineering, Math) students.

Compared with Fields Medals (equivalent to Nobel Prize in Math), the picture is reversed – where USA, France and UK are top. The secret lies in the formula : the multiplying factor – (* French), ie the math theoretical foundation notably in French Math.

Note: 2 Chinese Fields Medalists are listed in the nationalities of “British / HK, now China” (ST Yau 丘成桐), Australia (Terence Tao 陶哲轩 ).

# What is math?

What is Math ? Interesting article below:

https://infinityplusonemath.wordpress.com/2017/06/17/what-is-math/

• Mathematics = “that which is learned“ –(Pythagoras)

Math is not about calculation, it is understanding the nature, the universe, the philosophy (logic, intelligence – both “human” and “artificial”)…

What is Axiom, Lemma, Proposition ? Why rigorous Calculus was needed hundred years after Newton & Leibniz had invented it – “Epsilon-Delta” Analysis.

Difference between Riemann Integral & Lebesgue Integral ?


text:
# Stability results for nonlocal geometric evolutions and limit cases for fractional mean curvature flows

created by cesaroni on 04 Mar 2020
modified by novaga on 30 Jun 2021

[BibTeX]

Published Paper

Inserted: 4 mar 2020
Last Updated: 30 jun 2021

Journal: Comm. Partial Differential Equations
Volume: 46
Number: 7
Pages: 1344-1371
Year: 2021

ArXiv: 2003.02248 PDF

Abstract:

We introduce a notion of uniform convergence for local and nonlocal curvatures. Then, we propose an abstract method to prove the convergence of the corresponding geometric flows, within the level set formulation. We apply such a general theory to characterize the limits of $s$-fractional mean curvature flows as $s\to 0^+$ and $s\to 1^-$. In analogy with the $s$-fractional mean curvature flows, we introduce the notion of $s$-Riesz curvature flows and characterize its limit as $s\to 0^-$. Eventually, we discuss the limit behavior as $r\to 0^+$ of the flow generated by a regularization of the $r$-Minkowski content.


text:
# Java Program to Print first letter of each word using regex

In this article, we will understand how to print first letter of each word using regex. A regular expression is a sequence of characters that forms a search pattern. A regular expression can be a single character, or a more complicated pattern.

A regular expression helps you match or find other strings or sets of strings, using a specialized syntax held in a pattern. They can be used to search, edit, or manipulate text and data.

Below is a demonstration of the same −

Suppose our input is

Input String_1: Java Program
Input String_2: Joy of learning

The desired output would be

Result_1: JP
Result_2: Jol

## Algorithm

Step 1 - START
Step 2 - Declare two string values namely input_string_1 and input_string_2. Declare a regex Pattern namely string_pattern and a Matcher object namely string_matcher.
Step 3 - Define the values.
Step 4 - Using a while-loop, compute string_matcher.group() to fetch the first letter of each word.
Step 5 - Display the result
Step 6 - Stop

## Example 1

Here, we bind all the operations together under the ‘main’ function.

import java.util.regex.Matcher;
import java.util.regex.Pattern;
public class Regex {
public static void main(String[] args) {
System.out.println("Required packages have been imported");
String input_string_1 = "Java Program";
System.out.println("\nThe first string is defined as: " +input_string_1);
Pattern string_pattern = Pattern.compile("\b[a-zA-Z]");
Matcher string_matcher = string_pattern.matcher(input_string_1);
System.out.println("The first letters of the string is : ");
while (string_matcher.find())
System.out.print(string_matcher.group());
System.out.println();
String input_string_2 = "Joy of learning";
System.out.println("\nThe second string is defined as: " +input_string_2);
Matcher string_matcher_2 = string_pattern.matcher(input_string_2);
System.out.println("The first letters of the string is : ");
while (string_matcher_2.find())
System.out.print(string_matcher_2.group());
System.out.println();
}
}

## Output

Required packages have been imported

The first string is defined as: Java Program
The first letters of the string is :
JP

The second string is defined as: Java Program
The first letters of the string is :
Jol

## Example 2

Here, we encapsulate the operations into functions exhibiting object-oriented programming.

import java.util.regex.Matcher;
import java.util.regex.Pattern;
public class Regex {
static void print_regex_string(String s) {
Pattern string_pattern = Pattern.compile("\b[a-zA-Z]");
Matcher string_matcher = string_pattern.matcher(s);
System.out.println("The first letters of the string is : ");
while (string_matcher.find())
System.out.print(string_matcher.group());
System.out.println();
}
public static void main(String[] args) {
System.out.println("Required packages have been imported");
String input_string_1 = "Java Program";
System.out.println("\nThe first string is defined as: " +input_string_1);
print_regex_string(input_string_1);
String input_string_2 = "Joy of learning";
System.out.println("\nThe second string is defined as: " +input_string_1);
print_regex_string(input_string_2);
}
}

## Output

Required packages have been imported

The first string is defined as: Java Program
The first letters of the string is :
JP

The second string is defined as: Java Program
The first letters of the string is :
Jol


text:
# Writing Sparse Arrays¶

In this tutorial you will learn how to write to sparse arrays. It is highly recommended that you read the tutorials on sparse arrays and tiling first.

 Program Links quickstart_sparse writing_sparse_multiple writing_sparse_global

## Basic concepts and definitions¶

Query

Writing to TileDB arrays is performed by creating and submitting query objects (the term is adopted from the domain of Databases). The query carries the user buffers that contain the cell values to be written, along with the layout of the values in the buffers.

Query layout

The query layout determines the way the user provides the cell values to be written. TileDB supports two layouts for writing in sparse arrays.

Updates in TileDB are simple write operations. TileDB does not perform writes in-place, i.e., it does not overwrite previously created files. Instead, it creates new files, i.e., all files in TileDB are immutable.

## Writing to a sparse array¶

Let us revisit the quickstart_sparse example of tutorial Sparse Arrays. Here is how we wrote to the array:

C++

std::vector<int> coords = {1, 1, 2, 4, 2, 3};
std::vector<int> data = {1, 2, 3};
Context ctx;
Array array(ctx, array_name, TILEDB_WRITE);
Query query(ctx, array, TILEDB_WRITE);
query.set_buffer("a", data)
.set_coordinates(coords)
.set_layout(TILEDB_UNORDERED);
query.submit();
array.close();

After preparing the cell values to be written, we construct an array object, effectively “opening” the array, i.e., preparing the array for writes (e.g., this loads the array schema from persistent storage to main memory). Then we create a query, specifying that this query will perform writes. Notice that the query type must be the same in both the array and query object. (i.e., TILEDB_WRITE in both cases). Next, we set the buffers for attribute a and coordinates to the query. These will be dispatched to TileDB along with the query. Note that the coordinates are necessary, as these specify exactly in which cells you wish to write the values.

Subsequently, we set the layout; this specifies the order in which you stored the cell values in buffers coords and data. Unordered here means that the cells are not given in a particular order. TileDB needs this information in order to sort internally and then store the values along the global cell order (recall that TileDB always respects the global cell order when writing the array data in physical storage). In this example it happens for the given order (row-major) to be the same as the global order. We will see in later examples that this is not true in general. For instance, if we had specified a 2x2 space tiling for the above array, the global order would be (1,1), (2, 3), (2,4). Below we explain that TileDB enables you to write also directly in global order, avoiding the sorting and boosting performance. Finally, we submit the query and close the array.

Python

ctx = tiledb.Ctx()
# Open the array and write to it.
with tiledb.SparseArray(ctx, array_name, mode='w') as A:
# Write some simple data to cells (1, 1), (2, 4) and (2, 3).
I, J = [1, 2, 2], [1, 4, 3]
data = np.array(([1, 2, 3]));
A[I, J] = data

We first create a sparse array object, which “opens” the array in write mode. This prepares the array for writes, e.g., it loads the array schema from persistent storage to main memory. Then we initialize two vectors I and J with the coordinates we wish to write. Note that each vector holds the coordinates along each dimension, i.e., I holds the row coordinates and J the column coordinates. The above code will write to cells (1,1), (2, 3), (2,4). The coordinates do not need to be sorted in any particular order, i.e., TileDB always considers the cell layout as unordered in this example. TileDB will sort internally the coordinates on the global physical cell layout prior to writing the values on disk.

TileDB of course allows you to submit multiple write queries to an array, and a query may update (i.e., modify) previously written values. Consider the example in the figure below, where we perform two writes to the same array.

When we read the array, as expected, we get the cells shown in the collective logical view produced by both writes, i.e., after cell (4,1) is added and cell (2,4) is modified in the second write. Running example writing_sparse_multiple, you get the following:

C++

$g++ -std=c++11 writing_sparse_multiple.cc -o writing_sparse_multiple_cpp -ltiledb$ ./writing_sparse_multiple_cpp
Cell (1, 1) has data 1
Cell (2, 3) has data 3
Cell (2, 4) has data 20
Cell (4, 1) has data 4

Python

$python writing_sparse_multiple.py Cell (1, 1) has data 1 Cell (2, 3) has data 3 Cell (2, 4) has data 20 Cell (4, 1) has data 4  Let us see how the array directory looks like after the execution of the program: $ ls -l writing_sparse_multiple/
total 8
drwx------  5 stavros  staff  170 Jun 22 15:27 __35a9e44618d34f68a20ec0b5a51d17eb_1529695666920
drwx------  5 stavros  staff  170 Jun 22 15:27 __5f38614a64d94b97b607125965db3bdd_1529695666925
-rwx------  1 stavros  staff  115 Jun 22 15:27 __array_schema.tdb
-rwx------  1 stavros  staff    0 Jun 22 15:27 __lock.tdb
$ls -l writing_sparse_multiple/__35a9e44618d34f68a20ec0b5a51d17eb_1529695666920 total 24 -rwx------ 1 stavros staff 90 Jun 22 15:27 __coords.tdb -rwx------ 1 stavros staff 110 Jun 22 15:27 __fragment_metadata.tdb -rwx------ 1 stavros staff 12 Jun 22 15:27 a.tdb$ ls -l writing_sparse_multiple/__5f38614a64d94b97b607125965db3bdd_1529695666925
total 24
-rwx------  1 stavros  staff   82 Jun 22 15:27 __coords.tdb
-rwx------  1 stavros  staff  104 Jun 22 15:27 __fragment_metadata.tdb
-rwx------  1 stavros  staff    8 Jun 22 15:27 a.tdb

Notice that now there are two subdirectories under the array directory. Each subdirectory corresponds to a write operation and is called fragment. We discuss fragments in more detail in a later tutorial. However, what is important here is that the cell values added by different operations create different files and no file is overwritten. You may perceive each write as a separate array (hence, array “fragment”). TileDB is smart enough to understand how (and when!) you created these fragments and provide you with the correct values upon reading.

Note

Every file in TileDB is immutable!

A final remark concerns deletions. Currently, TileDB does not support deletions. If you wish to delete a cell, you will have to essentially set a “dummy” value (that you know how to recognize on your end) to that cell, which will act as a tombstone marking the cell as deleted. We are currently working on a better way of handling deletions, which we will make available in a future release.

## Writing in global layout¶

Warning

Currently global writes are not supported in the Python API.

So far we have been using the “unorderded” layout when providing the cells to TileDB for writing, which will be the most frequent layout you will use. However, if your cells are already laid out in the global order of your array, TileDB allows you to write them in the global layout. This provides two benefits: (i) you avoid the internal TileDB sorting step, which may result in some performance speedup (TileDB parallelizes sorting internally, but you can still gain if you completely avoid it), and (ii) as we shall see below, writing in global order enables you to submit an arbitrary number of queries, without creating a new fragment each time, but rather always appending to the same fragment. This is useful if you have a very large dataset and you wish to just stream it into a TileDB array, avoiding the creation of numerous subfolders and files.

You set the global layout simply as follows:

C++

query.set_layout(TILEDB_GLOBAL_ORDER);

In the writing_sparse_global example we show you how to slightly modify quickstart_sparse, such that you write in global layout instead of unordered, submitting two write queries instead of one. Here are the two write queries for the same three cells:

C++

// Submit first query
std::vector<int> coords_1 = {1, 1, 2, 4};
std::vector<int> data_1 = {1, 2};
query.set_buffer("a", data_1).set_coordinates(coords_1);
query.submit();

// Submit second query
std::vector<int> coords_2 = {2, 3};
std::vector<int> data_2 = {3};
query.set_buffer("a", data_2).set_coordinates(coords_2);
query.submit();

Observe that, if the next cell values to be written are stored in different buffers, you need to set those buffers to the query before submitting it.

When writing in global order, TileDB maintains some internal state. This is to allow you to submit successive queries and let TileDB pick up the writing process from where it left off. It is extremely important to flush this state when you are done writing in global order as follows:

C++

query.finalize();

Let us compile and run the program, and then inspect the contents of the array directory:

$g++ -std=c++11 writing_sparse_global.cc -o writing_sparse_global_cpp -ltiledb$ ./writing_sparse_global_cpp
Cell (1, 1) has data 1
Cell (2, 3) has data 3
Cell (2, 4) has data 2
\$ ls -l writing_sparse_global/
total 8
drwx------  5 stavros  staff  170 Jun 22 16:29 __01b96bab96a64c3b86e06417c16b0618_1529699391758
-rwx------  1 stavros  staff  115 Jun 22 16:29 __array_schema.tdb
-rwx------  1 stavros  staff    0 Jun 22 16:29 __lock.tdb

As expected, the array contains the same cells and values as quickstart_sparse. Moreover, despite the fact that we submitted two write queries, only one subfolder/fragment got created. This confirms that successive write query submissions in global order append the cell values to the same fragment files.

## Choosing a layout¶

In the above example, the global order was trivial to determine, because we had a single 4x4 space tile and the cell order was row-major. This resulted in a global order that required all cells to be sorted in row-major order. However, for larger arrays with finer-grained space tiling, it will generally be non-trivial to manually derive the global order and provide the cells to TileDB sorted on that order. Therefore, we expect you to use the unordered layout in the vast majority of your applications. Just note that TileDB has got your back here, since it performs sorting internally very efficiently via parallelization, whereas it also provides an efficient fragment consolidation mechanism in case you create too many fragments (covered in a later tutorial).

## Writing and performance¶

As mentioned above, the layout in which you write the cells may affect performance, as writing in the unordered layout involves some internal sorting, which is avoided in the case of global order writes. Moreover, each write in the unordered layout produces a separate fragment. We will soon explain that numerous fragments may impact both the write and read performance. See the Introduction to Performance tutorial for more information about the TileDB performance.


text:
## Lesson goal: Add fractions using Prolog

Previous: Counting in Prolog | Home | Next: Divisibility rules

Let's write some Prolog that will add fractions together. This takes a bit of logic, as you may remember from your math class.

Suppose you have two fractions $N_1/D_1$ and $N_2/D_2$, where $N$ means numerator and $D$ means denominator. The $1$ and $2$ refer to fractions $1$ and $2$ to add together, so we'd like to find $N_1/D_1+N_2/D_2$.

You probably remember the plan:
• If the denominators are the same, or $D_1=D_2$, then the sum will have this denominator, with the two numerators added together. This means $N_{sum}=N_1+N_1$ and $D_{sum}=D_1$ (or $D_2$). The answer will be $N_{sum}/D_{sum}$.

• If the denominators are different, or $D_1\ne D_2$, we'll have to find a common denominator $D_{sum}$, which is $D_{sum}=D_1\times D_2$. The numerator of fraction 1 will become $N'_1=N_1\times D_2$, and the numerator of fraction 2 will become $N'_2=N_2\times D_1$. Now, the numerator of the sum will be the sum of the new numerators, or $N_{sum}=N_1'+N_2'$. Once again, the answer will be $N_{sum}/D_{sum}$.
As an example, if the denominators are the same, as in $1/5+2/5$. The answer will be $3/5$. If the demoninators are different, like $2/3+1/4$, the $2/3$ will become $8/12$ and the $1/4$ will become $3/12$. The answer will be $8/12+3/12=11/12$.

As for Prolog, we'd like the goal to be something like add(1,5,2,5,Nsum,Dsum). for which we'd like Prolog to find Nsum to be 3 and Dsum to be 5. For something like add(2,3,1,4,Nsum,Dsum)., we'd like Prolog to find Nsum to be 11 and Dsum to be 12.
add(N1,D,N2,D,Nsum,D):- Nsum is N1 + N2.
add(N1,D1,N2,D2,Nsum,Dsum)
Move the mouse over a dotted box for more information.

#### Now you try. Finish the code for the fractions with different denominators.

Type your code here:

See your results here:


text:
A. Two Regular Polygons
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given two integers $n$ and $m$ ($m < n$). Consider a convex regular polygon of $n$ vertices. Recall that a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

Examples of convex regular polygons

Your task is to say if it is possible to build another convex regular polygon with $m$ vertices such that its center coincides with the center of the initial polygon and each of its vertices is some vertex of the initial polygon.

You have to answer $t$ independent test cases.

Input

The first line of the input contains one integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The next $t$ lines describe test cases. Each test case is given as two space-separated integers $n$ and $m$ ($3 \le m < n \le 100$) — the number of vertices in the initial polygon and the number of vertices in the polygon you want to build.

Output

For each test case, print the answer — "YES" (without quotes), if it is possible to build another convex regular polygon with $m$ vertices such that its center coincides with the center of the initial polygon and each of its vertices is some vertex of the initial polygon and "NO" otherwise.

Example
Input
2
6 3
7 3
Output
YES
NO
Note
The first test case of the example

It can be shown that the answer for the second test case of the example is "NO".