Mathematics - 2016-12-15 (page 4 of 5)

haha, I get that

It's a chance to express your creativity :P

@KajHansen but the creative part was done by the instructor

we are left to fill in the gaps

@KajHansen as you are learning about reps of finite groups

Fair enough

6:41 AM

here is an nxn matrix mult algorithm based on rep theory of finite groups done in less than n^3 operations

arxiv.org/pdf/1612.02896.pdf

it is a very recent paper

but great because it could lead to matrix multiplication being done in n^2

(all theoretical probably not of practical interest)

huh, interesting

this is complementing a paper from 2002 where it was stated it could possibly be done

then in 2005 some mathematicians latched on showing it was equivilent to the sunflower conjecture in combinatorics

now this came out

What a name

wait

that is not the correct arxiv paper

copy paste has not worked

haha

6:46 AM

wait no it is correct

wait no

not its nto

:D

arxiv.org/abs/1612.01527

here we go

copy and pasting paper into computer is hard

and don't be worried that you don't understnad anytinhg

just know there are brave men and women on the front lines using rep theory of finite groups

This is cool. I didn't know other matrix multiplication algorithms existed

yes strassen in the 80s showed it could be done in less than n^a with a around 2.7

here is the 2005 paper I was talking about arxiv.org/pdf/math/0511460v1.pdf

Very cool. I'll look into this further. It's intriguing that better multiplication algorithms than the standard one exist.

6:54 AM

and the original paper from 2002 arxiv.org/pdf/math/0307321.pdf

Here is a nice outline of said algorithms btw @KajHansen en.wikipedia.org/wiki/…

no that is not nice

incorrect link

here is the correct link en.wikipedia.org/wiki/Matrix_multiplication_algorithm

That did have this tho en.wikipedia.org/wiki/Exponentiation_by_squaring

under the heading sub-cubic alg

That was one of my favorite things I learned in undergrad. It's so simple

That is the exponent of matrix multiplication complexity

"2" being the lowest possible?

7:00 AM

conjectured

which is what this group theoretic approach aims to do

its gotten to strassens 2.8

2.4ish it looks like

yes

the papers should be more specific than I am :P

naturally lol

or if you are a group theorist

canonically

Ah, yeah lol

7:05 AM

wow my eye sifht has gone to shit

I just took my lenses out so I am considered legally blind

which is an adulteration

exasperating

I have pretty bad eyesight too

exaggerating

exaggeration

there we go

:D

it shows my reliance on spell check

You spelled all the words right :)

7:08 AM

its even worse than I thougbt

I'm not supposed to even by short sited

Well I guess loss of sight is 'god's way of stopping us from looking at 'the book'

I hear it had a chapter on rep theory @KajHansen

"the book"?

Of course

quoting Erdos

mhm

@KajHansen what is your email? (incase of nuclear disaster or further discussion of matrix multiplication)

kah13176@gmail.com

7:15 AM

Actually my notion of 'going back to primitive ways' shows I am infact modern

haha, email's only been a thing for like 20 years

@KajHansen it didn't seem to work

That's definitely my email

no doubt about it

nope I am blind

check your email

Yep, got i

t

7:18 AM

my I had sent messages highlighted

Cool, got your newest message. I'm going to go to bed, but I'll read and think about it further when I wake up again

@KajHansen in which case I will further it as I have assumed dialog. Ill make it pretty and everything for your morning wake

Sounds good. You should get some sleep too at some point

Night @Kaj @Ali

Good night Ted. Be back soon

7:28 AM

@TedShifrin are you off as well ?

Not yet. Should I be?

Hi

Hi, Kishore.

@TedShifrin I was wondering why you said bye to me LOL

Cuz you need sleep, Ali :D

7:30 AM

I don't know how time zones work. Judging by the day light, I don't know how time works either

What's going on, I mean discussion?

We should live relativistically?

Meaning?

What do you have to discuss, Kishore?

Let me check :D

7:32 AM

That was because Ali doesn't know how time works.

@TedShifrin my manifold is 3 dimensional

So what?

i just dropped a time dimension thats all

What is your manifold, rigorously?

No, you live on a 3-D submanifold in space-time.

7:35 AM

I now have cross products so thats interesting

<3

What is less than three?

actually 7 dimensions also has a cross product sort of

my lack of love for you guys

it's zero, in fact

What?

7:36 AM

yeah.

it just happened.

The lack is zero?

yes sir.

So you love us maximally?

physics is a submanifold of a g2 manifold

I am happy here

@Jason Globally, in fact.

7:37 AM

@MickLH Tasty!

@TedShifrin I think it's time I am slapped and put to bed

LOL

what..

What does that even mean?

Good night everyone

night

7:38 AM

Good morning people around me

Good night Ali.

Night!

Sleep well!

I will

"Good morning people in my neighbourhood (literally)." - Ali

7:41 AM

no offense guys, but thank you @TedShifrin for hanging around here

Why would that offend anyone?

Sorry, first time here, I don't know the culture.

idk people get jealous

I don't think it's the culture here specifically

just humans... they are weird, man

I see, I am quite weird too.

What do you study MickLH?

welcome! btw

Thank you.

7:44 AM

@Jason I actually dropped out a long time ago, but I do electrical engineering so I have to study ODEs and laplace transform shit and I enjoy Cryptography in my free time so I study number theory

Dunno why you said that, @MickLH, but no prob.

Well Ted, I still haven't made it through your book

er, Prof Shifrin

LOL

I see. I've had many friends drop out, and they still study too, some of them were better than I am at math. Electrical engineering sounds fun.

Ted you taught algebraic geometry :O?

To be honest if I took your class, I'd probably call you "Sir Schwift" with a positive connotation. I'm racist, I like russians lol

all my professors hated or loved me

no neutrals

7:47 AM

I like students who engage and work hard. Well, liked.

More differential geometry, but some complex algebraic geometry stuff ... Mostly undergrads, @Jason.

@ Ted Shifrin . Do you know about Serre's twisting sheaf?

You mean the scheme version of the canonical bundle?

I believe so, or it might be the anti-canonical.

I think canonical. I really never thought much about stuff outside the complex setting.

And I no longer own Hartshorne.

What is $O(1)$ in the scheme theoretic sense?

7:53 AM

oooh! oooh! raises hand Big-O notation??

No, Mick.

fuck dies in shame

It's defined in terms of Proj, no doubt. Don't ask me :)

Sure thing, I guess I am just finding this content harder than normal, or less well written, hard to discern which.

Don't be such a drama queen, Mick :D

7:56 AM

lol! I'm doing my best not to! I'm probably still doing it but I filtered as well as I can, sorry

:)

8:09 AM

What do you mean?

Something roughly along the lines of music "feeling right" when it sets up a problem and solves it for you in sonic representation

Concrete example: As a producer I've intuitively learned to minimize the L2 deviation of each frequency component's amplitude from the average amplitude, but at the same time regularize by a weird arbitrary "human hearing" function

It's really simple, but so few people do it

But the people who do consistently get comments along the lines of "it sounds so clear!"

Could I hear a sound sample with and without this modification, our of curiosity @MickLH?

Sure do you have a sample in mind?

and keep in mind, I'm not exactly the greatest, I'm basically just gonna do "Integration by graphing" lol

I don't have one :P.

Should I find one? What is acceptable?

I imagine songs that are already produced are too pre-edited or something?

Usually finished songs have already been visited by a producer who at least approximated such a transform to within a constant factor to keep their clients from yelling :P

I'll share what I'm working on hold on lol

8:26 AM

With the non-edited version also?

@Jason here's the "raw" version, I mean you probably won't like my songwriting but oh well lol drive.google.com/open?id=0BxOUlWYj0c6tenhzY1R3N1o2dUU

and here's a roughly optimized version of that exact raw wave: drive.google.com/open?id=0BxOUlWYj0c6tZzJONkJwVVkyUjg

when I say "rough" I really mean it lol, I've found that you only need 3 to 5 frequency intervals to achieve a pretty clear result to a human ear

So I just used some time domain filters to split up the sine waves by frequency, and then adjusted the volume by a windowed average

I'm inebriated. Don't judge my vibe atm.

8:48 AM

(fyi future visitors, I threw that stem away, don't listen)

it was meh

Joris

Hi, I didn't receive an answer last time, so I am reposting: I would like to (seriously) study Algebraic Geometry, and I am looking for a study partner. I imagine, for example, that we meet on Skype (at least) once a week and discuss the exercises and maybe lectures contained in the 2002 lecture notes by Andreas Gathmann. Where, besides here, is a good place to post this? Is it appropriate to ask a question on the main page?

@Joris If you'll erase the beginning, "Hi, I didn't receive an answer last time, so I am reposting:" so that the first few words contains "study partner" I would pin it up on the right side of the chat

Joris

Thank you!

I would like to (seriously) study Algebraic Geometry, and I am looking for a study partner. I imagine, for example, that we meet on Skype (at least) once a week and discuss the exercises and maybe lectures contained in the 2002 lecture notes by Andreas Gathmann.

3

someone put a $θ(n^2)$ matrix multiplication algorithm on the arxiv arxiv.org/abs/1612.04208

10:11 AM

@DHMO hi!

hi

what are a,b, and c?

I got till here

@Sophie in a triangle……

@DHMO how to do ?

I don't understand the question

10:17 AM

@DHMO in triangle ABC exradii are in the ratio of (kr1:llr2:mr3) then ratio of sides (a:b:c)=?

what is k l m r1 r2 r3?

r1 =∆/(s-a) r2=∆/(s-b) and r3=∆/(s-c)

:(

@DHMO got?

kr1 = lr2 = mr3
k∆/(s-a) = l∆/(s-b) = m∆/(s-c)
Let (s-a)/k = (s-b)/l = (s-c)/m = p
s-a = kp, s-b = lp, s-c = mp (*)
3s-a-b-c = (k+l+m)p
s = (k+l+m)p
From (*): a = s-kp = (l+m)p; b = s-lp = (k+m)p; c = s-mp = (k+l)p
Therefore a:b:c = (l+m):(k+m):(k+l)

@Ramanujan

@DHMO thanks

Mary Star

11:39 AM

When $x$ is a large negative number, we have that $-1<1/x<0$, right? Does it hold then that $\left [1/x\right ]=0$ ?

We have then numbers of the form -0,00011111 for example. The integer part is then 0, or not?

@MaryStar, define "integer part"?

Is [ ] just the floor function?

Mary Star

I thought that when we have a negative number it is the ceil function... Isn;t the integer part of a number of the form "a,bcd...." equal to "a" ? @AntonioVargas

I don't know that "integer part" has a standard definition. Does it?

Just use ceiling and floor, everyone would understand that way

Akiva Weinberger

11:56 AM

@TedShifrin What about its negative??

Functions with jump discontinuities are piecewise continuous functions, right?

Id say so

Szabolcs

12:18 PM

What is the usual terminology to use to distinguish induced subgraph isomorphism from "plain" subgraph isomorphism?

user123733

Could anyone help me out in this

0

Q: property of ellipse

In my book there is an statemet for a ellipse . Refering to (x/a)$^2$ +(y/b)$^2$ =1 The statement is The product of the length of the perpendicular segmets from the focii on any tangent to the ellipse id b$^2$ and the feet of perpendicular lie on its auxilary circle and the tangents at the...

conic-sections

Ilan Aizelman WS

Help pls math.stackexchange.com/questions/2057200/…

mick

Bounty here : math.stackexchange.com/questions/1553888/…

12:41 PM

damn hydra game

1:05 PM

I thought this week was already next week. I'm going loony.

GFauxPas

1:41 PM

This week is next week, you're not crazy, everyone else is

@GFauxPas greetings

Bman72

2:16 PM

Are you never tired of mathematics? I'm sitting right now in front of a desk at the university, trying to find the motivation... Has some ever felt like me?

hey guys, i have a question
if f is function; continuous on R, and is also differentiable
lim f '(x) as x approaches infinity would equal what ?

Bman72

@MohamedZiad is precisely 5.

@MohamedZiad Just kidding, may be 6

@MohamedZiad it may be anything

Bman72

@MohamedZiad It might be anything. Consider for instance some polynomial functions. ;-)

well i was saying it is undefined
how could it be anything ?
infinity should indicate to the last end of f where f can't be differentiable ?

i want to be corrected if iam so :S

2:43 PM

@MohamedZiad Without more information you can't say anything. Look at $f(x) = 1/(1+x^2)$. The limit of $f'$ towards infinity is $0$.

can anyone tell whether this is true? arxiv.org/pdf/1612.04208v1.pdf

interesting result

@Bman72 Of course. In that situation I play Rocket League.

Indeed

Hi everyone

What does $u_n = \theta(n^2)$ stand for here ? does it mean like $a n^2 \le u_n \le b n^2$ for some positive constants a and b ?

2:58 PM

@Astyx strictly positive constants, yes

does this result imply that's impossible? dl.acm.org/citation.cfm?doid=509907.509932

Thanks

@BalarkaSen i am really sorry if this would sound silly as am still in my calculus 1
do i treat the function f'() as an absolutely new function ? what i mean is :
when a function defined on a closed interval, what i know is that the derivative of this function at the first and the last numbers of the intervals is undefined as the limit of the function doesn't exist at such points .. is the same thing applied with infinity or what do we apply ?

If this is true it surely is very interresting

@MohamedZiad, consider $f(x) = ax$, where $a$ is some real constant. What's $\lim_{x \to \infty} f'(x)$?

@MohamedZiad Sure, but, $\Bbb R$ is not the same as a closed interval. Derivative of the function at endpoints of an interval literally does not make sense because you can only take one-sided limit.

But $\lim_{x\to \infty} f'(x)$ is a perfectly well-defined notion. It may be $\pm \infty$, or it may not exist, but it's well-defined unlike the previous thing.

Mary Star

3:01 PM

Could we calculate the limit $\lim_{x\rightarrow 0}\frac{\sin (x)-x+x^3}{x^3} $ also using the squeeze theorem?

What is the squeeze theorem @MaryStar ?

@Astyx $f(x)<g(x)<h(x)$ and $\lim_{x\to c}f(x)=\lim_{x\to c}h(x)=l$ imply $\lim_{x\to c}g(x)=l$

Oh right thanks

Hi @Alessandro

How're you doing with numerical analysis? :D

@MaryStar How do you intend to use that theorem to help you here ?

3:08 PM

We implemented some numerical methods for ODEs today, I find the professor teaching programming much clearer than the theory one, so it was fine @Balarka

Also today I discovered that I believed in something false during a topology class!

@Sophie Do you happen to know what $a_1, a_2, \dots$ stand for in the paper ?

not yet

Oh right I see

They convert the matrix to a vector

do you know why he picked $n=100$?

In a metric space the boundary of the open ball of radius $r$ and center $x$ is not necessarily the set of points whose distance from $x$ is exactly $r$, even if there are such points

Ilan Aizelman WS

3:10 PM

Could someone help please? math.stackexchange.com/questions/2057200/…

@AntonioVargas it should equal a
@BalarkaSen so i don't treat infinity as the end point of the function ? that's what ur trying to say right ? the derivative at infinity would be an indication of the behavior of the function when x is sufficiently big ?

Should have read the beginning before asking ^^

Not yet

I guess it has to do with primes

44 would have sufficed to satisfy that inequality

They surely didn't want to be too specific about that

@Alessandro Ah, yes.

3:12 PM

The order of magnitude would be 100

I'm afraid he just used a big round number

I had never thougth about it, but it seemed very plausible, until we saw a counterexample that is!

@MohamedZiad I don't really understand what you're trying to say.

part 3 doesn't seem very readable to me

@Alessandro {0, 1} with the discrete metric does it, right? The open ball of radius 1 around 0 is {0}, which is closed too, so the boundary is trivial.

3:20 PM

@BalarkaSen i will try to rephrase using my few knowledge
what i am trying to say is that my expectations was that infinity is the point where the function f ends, so this would make me evaluate the derivative of the function at infinity as undefined and does not exist .. that's where i am wrong right ? and what i concluded from what u said is that the derivative of x exists as we don't know where it is, infinity is just an expression for a big number where x have a big enough value

did i understand you or?

CausingUnderflowsEverywhere

For one, infinity is not a number, so "evaluate the derivative of the function at infinity" does not even make sense, let alone being undefined or nonexistent.

$\lim_{x \to \infty} f'(x)$ on the other hand is well-defined. It might or might not exist depending on what $f$ is.

woahhhhhhhhhhhhhhhh this means if I can convert 100 / (2 * 5) into (100/5) /2 , then I just rearranged stuff in brackets by finding the equivalent! I've never messed with brackets yet they've always been static @AkivaWeinberger

Looks good @Balarka the example we saw was the set of binary sequences with distance given by $2^{-n}$ where $n$ is the first entry in which the 2 sequences are different

is a plane plus a point at infinity homeomorphic to a sphere?

CausingUnderflowsEverywhere

Ah

3:24 PM

sorry but infinity is not a point,

@Sophie Modulo knowledge of what neighborhoods at the point at infinity are.

@BalarkaSen thank you :)

And the open ball centered at (for example) $(0,0,0,0...)$ and radius 1/4 is both open and closed

Right.

@MohamedZiad $\lim_{x\to +\infty} f'(x)$ is not $\lim_{x\to +\infty} {f(x) - f(+\infty)\over x - \infty}$ firstofall because that makes no sense at all.
Instead $f\mapsto \lim_{x\to +\infty}f(x)$ is a function from the set of numerical functions that have a limit at $+\infty$ to the set of reals. Then $\lim_{x\to +\infty}f'(x)$ is nothing more than the limit of the derivative function of $f$ at $+\infty$ (and it has "nothing to do" with what $f$ gets close to at $\infty$)

There exists things called compactifications of $\Bbb R$ that let you assign values to $f$ at $+\infty$ or $-\infty$, but these do not always (as in, they generally do not) respect the limit of derivatives

3:31 PM

@BalarkaSen define the distance to the point at infinity to be the inverse of the distance from the origin

@Astyx thanks for helping me, and yeah, i just understood where my confusion came from , thanks anyway ^^

@Sophie Then that's correct

woah

ofc that doesn't actually define a metric, but the idea stands

bah! Trivialities

stereographically project the plane to a sphere and call the bottom 0 and the top infinity. Define distances as the lengths on the surface of the sphere

3:42 PM

yup

finally got off my ass and started on spectral sequences

"Trolling Euclid" by Tom Wright is the funniest thing I ever read

good man

Danu

So @MIkeMiller the 4-manifolds course is getting to the moduli space-part

:)

Danu

3:56 PM

But the lecturer (substituting for Kotschick, who is away this week) doesn't really know how this crucial Banach manifold stuff works

For the story you don't need to

Danu

So it's a little bit qualitative, for now.

Things like the inverse function theorem on these spaces and such, and we use it to get that the moduli space is (near an irreducible point $(A,\Phi)$, $\Phi\neq 0$) is a smooth manifold