Get in here if you like algorithms. Basic discussion and any thoughts about algortihm design, implementation, problems etc. are all welcome.
I'll start with a question to get you in the mood.
Let's suppose there is a city map and I set a random starting point somewhere on it.
Is it possible to design a path structure (such as go left then right then straight for 2 blocks and left again) that will ensure that I am getting a simple random sample (equal selection probability / inclusion probability > 0 for all i in n) out of all city households?
If so, how would the algorithm look like?
>>8558387
Easy.
Works on both regular grids and arbitrary graphs:
1. Let n = number of possible nodes to move to next.
2. Roll 1 n-sided die
3. Move one step in the direction suggested by 2.
4. Go to 1.
>>8558396
That is a correct solution. Exactly what I had in mind.
Let's modify the task a little to make things harder. Realistically spoken, there is more than one person in each household. Suppose you want to generate a random sample of the people living in the city, not a random sample of the households. There might be different amounts of people in said houses.
How do you proceed now?
>>8558413
Naive answer but often good enough in practice: weigh the sides of the die in proportion to the number of people in each household.
Also, I realized that I was technically incorrect in saying that the method works for arbitrary graphs, since the graph structure would cause the probability of reaching an isolated node (say) to be lower than that of an equivalent centralized node.
And we would probably have to require at the very least that the graph be connected.
One possible approach to this might be to draw up the incidence matrix M of all nodes in the graph, let p = (p1,...,pN) be the desired probability distribution of node hits, replace each of the '1' entries in N with arbitrary variables, and solve the characteristic polynomial Np = p <-> |N - I| = 0 for any set of non-negative weights to use at each junction, such that the long-run sample probabilities equal the Perron-Frobenius root p.
That said, I'm not sure if the coefficients can always be found for connected graphs (it clearly cannot for unconnected graphs), or if finding such coefficients could be done in a more tractable way.
Also, it's late where I am and I'm going off to sleep now. Good luck with your thread and hopefully it generates some interesting discussion before I check back.
Hey /sci/ I took this picture a while ago but I never figured out why the clouds were formed in this shape and direction. For as far as you can see in the picture, they seem to be pointing in the direction the plane is flying. That may just be a correlation and not the cause. Why are the clouds like this?
>>8558381
It's called lee wave. It has nothing to do with the plane.
https://en.wikipedia.org/wiki/Lee_wave
>>8558400
holy fuck that is cool
damn maybe i should study physics or aerodynamics
thanks
How can thesd clouds be real if our eyes aren't real?
Is doing maths in colours really helpful? A friend of mine insists on taking ntes in colours and arrows and all of that visual stuff. When i look at his notes i get really confused because it's all colourful and i don't understend very well. Is it helpful or it's just a waste of time and creates confusion. Pic kinda related, my friend is actually worse.
>>8558215
dear god do people actually spend this much time writing down such trivialities? and don't tell me it's a kid who did this because we all know it's 22yo jessica who's taking this "impossible math class" alongside her sociology BA
>>8558215
and to answer the question, no don't take notes in color. in fact, do not take notes at all. unless you're taking a phd math class (and even then…), everything you need to know has be written down in 20 different books. just go to the library.
>>8558215
Nah it's pure autism.
> be me, a very lost soul
> Can't decide if I want to major in ME or EE.
> Want to design and build robots.
> I also have dreamed of starting my own dynamics/R&D company, what would it take to do this?
Plz educate me.
Doesnt matter which you pick, but I'd say EE since it has more math. Either way you'll find that 60% of your courses won't be helpful for robotics, only a few in the beginning and at the end deal with relevant material.
Also if you take ME you'll have to learn some EE and vice versa. Basically it doesn't matter which path you take since Robotics = Mechatronics = ME+EE+CS
>>8557940
Is mechtronics a meme degree? Can I just get that instead?
>>8557948
"I want to build robots" is exactly the same meme as "mechatronics degree", so sure
Is there any game that effectively stimulates your memory, reaction, intelligence, strategy and everything controlled by a competitive scenario? which would be That game?
>>8557778
Good question, bump
>>8557778
EvE online
>>8557778
the game of pushing your boundaries and discovering NEW things.
Google makes it SOOOOOOOOOOO hard to find new things.
Cool diseases thread
This one causes damaged tissue to regenerate as bone
OMFG SO COOL
pyoderma gangrenosum From Infiammatory bowel Disease, somehow the two thing are related
Today is a special day!
To commemorate that, can you solve this puzzle?
It's e.
Polite sage.
>>8557478
The answer is 3.
>>8557478
sqrt(9)
I don't understand the falling cat problem:
http://en.m.wikipedia.org/wiki/Falling_cat_problem
I guess the angular momentum being conserved makes sense. Does the cat have rotational energy though?
It seems to me that going from inverted (180 degrees) to upright (0 degrees) is a change in rotational position: theta (180) - theta (0) = 180 degrees. From rotational kinematics, we can determine the angular velocity of the cat during the inversion and we can also determine the angular acceleration. Hence the cat has rotational kinetic energy. I assume that energy comes from the chemical energy of the cats muscles. Is that right?
But the cat can keep doing this over and over. We could build an electronic cat which could start with 0 angular momentum and then spin 100 times a second. It seems odd to say, "No, that rapidly spinning cat has no angular momentum." Does it have angular kinetic energy? You can have angular kinetic energy and no angular momentum?
>>8557448
I solved the problem. Cats land on their feet because they change their shape.
>>8557473
So when they change their shape and invert themselves, do they have angular momentum during the process? Do they have rotational kinetic energy?
>>8557483
what....is your point...
Where to learn math on the internet? I'm
Inb4 gtfo underage
>>8556999
Race-baiting thread. Go away.
>>8556999
http://www.coolmath-games.com/
>Australia
lmao
shitposters BTFO lmao
How do I know practicing will make me better at something (say math)?
Everyone is always saying
>just practice moar problems lmao
But I have no evidence it works so it feels like a waste of time so whenever I decide to start doing it I lose motivation and end up procrastinating.
Does practicing a bunch of problems actually help understanding?
>>8556918
It depends on how you practice.
If you do basic ass problems that just require you to go through the motions that you already know how to do, then no. Practice is not helpful.
If you do problems that are difficult, or slightly too difficult for you, then practice is very helpful.
>>8556918
>Does practicing a bunch of problems actually help understanding?
Not if you don't get what you are doing.
I've seen some people practice and in my opinion they were at best guessing. That practice was useless because they learned nothing. They saw a new problem and tried to apply a procedure they saw in an example and then they get an answer... completely wrong by the way, and then they move to the next problem.
It works but only if you know what you are doing.
In my opinion practicing does not make you better, it makes you faster. So if you understand what an antiderivative is then practice so that you can become faster at computing them, which will be useful for the exams.
If you do NOT understand what an antiderivative is then DO NOT practice until you truly understand it. Go back to the definitions and maybe the elementary examples until you know what the fuck is going on. Understand substitution before you apply it like a retard, understand partial fractions before you apply like a retard.
>But I have no evidence it works
the more you practice shitposting the better you get at it. Haven't you noticed it?
Will electric motors ever be able to generate enough force to replace fossil fuels in areas like airlines and cargo ships?
What's the most promising source of energy when we inevitably run out of oil?
>>8556306
>Will electric motors ever be able to generate enough force to replace fossil fuels in areas like airlines and cargo ships?
Yes. Many ships already do use electric transmission, and the power-to-weight of modern electric motors is definitely high enough to replace the engines in propeller aircraft.
The hard part is generating the electricity to power the motors.
>What's the most promising source of energy when we inevitably run out of oil?
Hard to tell. That depends on geography, economics, and what technological advances we get to see.
>>8556306
>Will electric motors ever be able to generate enough force to replace fossil fuels in areas like airlines and cargo ships?
Motors aren't the problem, batteries are.
>What's the most promising source of energy when we inevitably run out of oil?
Electricity isn't an energy SOURCE. But if you mean energy CARRIER, I think batteries will gain prevalence in less energy-intensive applications, while more energy-intensive applications such as aviation will continue to use combustable fuels, albeit from non-petroleum feedstocks. Even fucking seawater can be turned into jet fuel if you pour enough energy into it: https://www.nrl.navy.mil/media/news-releases/2012/fueling-the-fleet-navy-looks-to-the-seas
>>8556317
I imagine you'd need a pretty big battery to fly a passenger plane for 14 hours straight.
>>8556321
I said it like that referring to a source of kinectic energy, but I guess you are correct.
Also that's a pretty interesting article, I don't understeand the actual science behind it of course but the fact that that's possible is pretty cool.
Makes me think...How comes those big ass ships don't have systems to produce hydraulic energy in some way? Or they do?
>be me taking Real Analysis
>"how to determine when you are allowed to switch limits" the course
Literally when am I going to use this?
>>8555376
when some crap artist russian professor of yours has you doing integrals all day long in complex analysis next year.
>>8555382
this, get ready for analysis 2 where you learn when you can switch limit and integral sign, and limit and summation sign
good times
Link here if you want it for free (http://www.people.vcu.edu/~rhammack/BookOfProof/)
>>8555004
I am not a fan in general of entire books just teaching you how to do a basic proof. A full coverage of rudimentary proof methods takes up about a chapter worth of pages.
The only real purpose of a book like this is padding out an "intro to proof" module into a full semester instead of two weeks.
This book in particular is worse at the same problems most of these have. The writing itself is padded to hell, the majority of the "proofs" they train you on are uninteresting bullshit (flip to page 103 for the eye-popping "if 7x+9 is even then x is odd") and the proofs themselves are written so stiffly that they make the hamburger method you learned in HS look avant-garde.
I'm using it as my first introduction to set theory and it seems alright so far. Its the only text I've seen with both exercises and solutions for set theory, which is nice.
>>8555055
I get where you're coming from but I think you know jus as well as I do that there are vast swathes of the population for whom elaborate, precise, logical argumentation which drives toward a particular conclusion is a strange and frightful enterprise, which requires slow development and hand-holding. Accepting this premise, I am therefore in support of these types of books existing, because about eighty percent of the population could actually use them, and say about fifty percent might actually get something out of one of these books if they internalize the ideas, even if it's just a rudimentary, albeit working, understanding.
That said, I have just one of these types of books on my shelf, bought as a curiosity once: Polya's How To Solve It. I've never read it, but I've flipped through it a few times and now I seem to remember why: /I already know all this stuff. I am not this book's core audience./
Can blood extinguish a fire?
it's >50% water, so I assume yes
>>8554443
Any substance that can effectively deprive fire of oxygen can extinguish it.
Think of it in terms of physics, a fluid such as water or blood basically function as a three dimensional blanket that chokes the fire out and prevents the reaction from continuing.
>>8554589
blankets are three dimensional already :^)
How can math be real if Russell's paradox is real?
t. Naive set theorist stuck in the 19th century
>>8550678
Mathfags BTFO
>>8550678
Look at this confident and smug mug, yet friendly. You can tell how intelligent he is. You can tell that this person had very deep thoughts.