Mathematics - 2013-02-22 (page 4 of 5)

Dominic Michaelis

20:00

i am fine and how are you ?

my theo exam was such a mess

@charlie still fine :D

J G

Has anybody used the EM algorithm before (Efficiency-Maximization)?

Peter Tamaroff

@Charlie $\sup$?

Charlie

I'm fine

anon

@JG yes, sometimes I go the diagonal of a rectangle instead of the perimeter when I'm walking

Charlie

@DominicMichaelis why?

J G

20:06

Oops. I meant expectations-maximization

NBP

Is there a reason why I'm not getting answers for a coupling question I asked? Is this not a known probability concept?

Peter Tamaroff

@anon @MarianoSuárez-Alvarez Hahha. Need some help!

J G

as in search.cpan.org/~avikak/Algorithm-ExpectationMaximization/lib/…

Peter Tamaroff

@anon HOw did the storm go?

anon

had to shovel snow
three times

Peter Tamaroff

20:07

Did you have no problems?

anon

thursday campus was closed

NBP

anon: we got no snow where I live.

Are you from scotland?

anon

otherwise no issues

midwest usa

Peter Tamaroff

@NBP Nebraska man.

NBP

Could anyone help me with a coupling problem?

Peter Tamaroff

20:08

@NBP Chocolate usually works.

NBP

Peter, I don't understand

you're saying eating choclate makes people think better and thus solve coupling problems?

anon

clearly you are not a romantic then!

Peter Tamaroff

You said you had a coupling problem...

NBP

that would be true for all mathematical problems I think

Dominic Michaelis

i never thought that a 2 x 2 matrix could ever be so ugly

NBP

20:09

I see no reason for this tip to be specifically useful for these type of problems

anon

a 2 x 2 matrix can be four times as ugly as any normal expression

2

it's a joke, not a tip

user58512

haha

Charlie

@DominicMichaelis what??

Peter Tamaroff

@anon Anon.

anon

Peter.

Arkamis

20:10

My solutions to coupling problems always begin with, "here, have this glass of wine first."

NBP

@anon, I've already found my one true love, so it's not that kind of coupling problem

Anyway, this is a mathematics channel, why would I address you guys with relationship issues

anon

not sure if serious

NBP

It should be obvious from context that I'm referring to a mathematics coupling problem.

specifically a probability space one

Peter Tamaroff

I have been given the following problem. Define a group on $\Bbb Z^3$ by summing coordinatewise in the following manner $$(x_1,x_2,x_3)\oplus (y_1,y_2,y_3)=(x_1+y_1+x_2y_3,x_2+y_2,x_3+y_3)$$

NBP

sorry for not being clearer anyway

so, could any of you guys help me with a probability coupling problem?

Charlie

20:11

@NBP we talk about everything here

NBP

@Charlie but it says mathematics..

anon

nbp, everything was clear from the start, you just need to get used to people having fun for the sake of having fun

Peter Tamaroff

@anon I have to show that this group is isomorphic with the group $G$ obtained by the relations $x_1x_2x_3=x_2x_1$, $x_1x_3=x_3x_1$ and $x_2x_3=x_3x_2$ on $FG^{(3)}$

anon

"rarely if ever expressible as the ratio of integers" was put in the room description for a reason :)

NBP

@anon, I figured mathematicians were above these sort of stuff. alas

Peter Tamaroff

20:12

Now, as I understand it, $G$ is $FG^{(3)}$ quoted by the normal group generated by the elements of those equations $=1$.

NBP

Can I link you to the problem?

anon

yes

NBP

@anon, math.stackexchange.com/questions/310848/…

Charlie

@NBP everything is math

Peter Tamaroff

Namely $x_1x_3x_1^{-1}x_3^{-1}$ &c...

NBP

20:13

it should be simple for men of your stature

though I see no algorithmic way to approach such an exercise.

anon

not sure if there's a probabilist in the room atm

NBP

@Charlie, I have never experienced anything physical that is math. in my opinion maths deals with abstract, pure concept

Dominic Michaelis

@Charlie mathb.in/2020

Peter Tamaroff

@NBP I think Didier Piau is boss at prob.

NBP

@anon, where can I find one?

Is he the guy who answered me?

Peter Tamaroff

20:14

He's user is "Did"

anon

@DominicMichaelis write the entries as a,b,c,d - solve for eigenvalues in terms of these, then plug in the expressions for a,b,c,d

NBP

Well, I think he misunderstood my issue

and now he's not responding

Peter Tamaroff

@NBP Yes.

He commented.

@NBP Do not upset him.

I think he's kinda moody =P

NBP

I didn't, sorry

Peter Tamaroff

"All you have to do now is to show size 4 is not possible. Assume Ω has size 4 and try to reach a contradiction."

Oh, you don't like that.

Charlie

20:16

@DominicMichaelis oh

Dominic Michaelis

@anon yeah it was in a theoretical physics exam

NBP

Well I couldn't do that, but that's really missing the point of my question (which is also why I didn't post the probability space I found in the first place)

Peter Tamaroff

@anon What do you think of my problem?

anon

@PeterTamaroff You want to define a map $F^{3}\to G$ such that the images of the $x_1,x_2,x_3$ satisfy the desired relations. My first guess would be to check out (1,0,0),(0,1,0),(0,0,1), and if adapt if need be.

NBP

@Peter Tamaroff, my biggest concern is not being able to assert that the cardinality of that probability space would be five, and it feels as if I found it by chance - and only then would it be viable for me to address the fact that 5 is the minimal probability space required.

Peter Tamaroff

20:17

@anon Yes, but then I'd have to quote by the kernel, yes?

@NBP Chance is good!

Many times we find stuff by chance.

NBP

Not when it's in an exam and you have 5 minutes to solve a problem

anon

then (given surjectivity), G would be iso to the quotient of F3 by the ker, yes

NBP

As happened to me

Peter Tamaroff

@anon Oh, yes. That is the basic of free groups plus the 1st iso.

Tim

@Ilya: Hello, can I ask a few quick questions regarding my two posts?

Peter Tamaroff

20:19

@anon Using $e_i$ in order we don't get what we want.

We get $(a,0,0)\oplus(0,b,0)\oplus (0,0,c)=(a+bc,b,c)$

I think $e_1,e_3,e_2$ does it.

Dominic Michaelis

you want a puzzle ?

Tim

1. in math.stackexchange.com/questions/309623/…, is my comment before the last one correct regarding Fubini's theorem and proving $f \in L^2([0,T]\times \Omega)$?

NBP

@Dominic Michaelis, no I haven't solved this coupling problem yet.

Peter Tamaroff

@anon Oh, great. If we set $x_1=e_1$, $x_2=e_3$ and $x_3=x_2$ we win.

anon

goodie good.

Peter Tamaroff

20:22

I actually tried first to set up equations using the defining properties.

Tim

2. In the same link in 1, in Ito's isometry, on its LHS, is the ito integral $∫^T_0 X_t dW_t$ a $L^2(Ω)$ function?

Peter Tamaroff

And solving for the coordinates.

But I think I messed up.

Oh, no wait.

I just didn't chose wisely.

Because I did get $x_1=(x,0,0)$

Tim

3. On the RHS of Ito's isometry, is $∫^T_0 X^2 dt$ a Lebesgue integral or something else? (I asked it here math.stackexchange.com/questions/311211/…)

Peter Tamaroff

and $x_2=(0,0,1)$

I think I messed up with $x_3$

@anon Thanks.

I proved the following.

Let $N_S$ denote the normal subgroup generated by $S\subset G$, $G$ a group.

Then set $^g S=\bigcup_{g\in G} g^{-1}Sg$.

We have $\langle ^g S\rangle =N_S$

NBP

@Peter Tamaroff, how do I contact this Did guy?

Peter Tamaroff

20:25

@NBP Comment on the post.

NBP

Can I have his phone number? maybe he didn't notice I commented again

Peter Tamaroff

Just ping him.

NBP

I did comment on the post

@Did

Peter Tamaroff

@NBP Whu? Just be patient...

NBP

@Did, are you here?

anon

20:25

@PeterTamaroff your union is called the normal closure operator (the intersection would be called the normal core operator). just trivia.

Peter Tamaroff

@NBP No, I never see him around.

@anon Oh, and why is it called like that?

NBP

@Peter Tamaroff, so pinging and commenting didn't help, where can I get his number?

anon

I have only seen him here a handful of times. But of course if pinged he will see it in his inbox.

Peter Tamaroff

Also, it is bad practice to write $^g S$ for that conjuation?

anon

@NBP random people over the internet don't often give their phone numbers to likewise random people

Peter Tamaroff

20:27

@NBP I don't have it, but I don't think he'll enjoy getting called and stuff.

He has a wwebpage. Google him.

Tim

I saw Didier once or twice in Chat room

I said hello to him

Peter Tamaroff

@anon Or their name [cough cough]

2 mins ago, by Peter Tamaroff

@anon Oh, and why is it called like that?

anon

@PeterTamaroff probably, yes. oftentimes group theorists will use $S^g=\{g^{-1}sg:s\in S\}$ and ${}^gS=\{gsg^{-1}:s\in S\}$ (this way $x\mapsto x^g$ is a right action and $x\mapsto{}^gx$ is a left action, which makes exponential notation easier with composition)

typing, dammit

NBP

@Peter Tamaroff, I'll be respectful and my english is pretty good

Peter Tamaroff

@anon Oh, OK. Sorry!

anon

20:28

>:<

(don't be too alarmed)

Peter Tamaroff

@anon And one is an homomorphism while the other is a antihomomorphism, or what was it called?

when $a(xy)=a(y)a(x)$

anon

normal closure gives the smallest normal subgroup containing blah, just like the topological closure gives the smallest closed group containing blah. the normal core is the largest normal subgroup contained within blah (as it is inside, it is a "core"). note that the normal and topological closure are distinct in a topological group.

yes, antihomomorphism

or "right automorphism" (also seen this term)

Peter Tamaroff

@anon But the normal group generated by $S$ is the union of the normal closure of $S$ over all the $g$s, yes?

So $gSg^{-1}$ is he smallest normal subgroup contianing $g$; right?

anon

oh, I suppose I am conflating the two, when technically the normal closure does not give you a subgroup generally

@PeterTamaroff why would it be normal?

no, conjugation and normal closure are different. normal closure is the union of all conjugates.

Peter Tamaroff

@anon Because $gg_i Sg_i^{-1}g^{-1}$ is also in the group?

@anon Oh, OK.

anon

20:33

@PeterTamaroff if $S$ isn't normal then $gSg^{-1}$ isn't normal

user58512

:(

anon

@PeterTamaroff if $x\not\in N_G(S)$ (the normalizer) then $gxSx^{-1}g^{-1}\not\in gSg^{-1}$

Peter Tamaroff

@anon How silly of me, I see it.

anon

there went my nap time

Peter Tamaroff

@anon Naps are for the weak!

Dominic Michaelis

20:35

nap? its called standby :D

3

Charlie

@DominicMichaelis hehehe

Hi @jacob

user58512

whats up

Tim

Any analyst willing to help?

user58512

with what

you'r advanced

user19161

@NBP Nobody calls someone else here on SE, unless they are good friends.

user58512

20:40

i cant help you

user19161

@Charlie Hello.

Tim

@user58512 The three questions starting at chat.stackexchange.com/transcript/message/8230231#8230231

Peter Tamaroff

Axiom: It is impossible to recharge a foutnain pen without getting stained.

user58512

sorry

user19161

@PeterTamaroff You use a fountain pen?

Tim

20:41

@user58512 I am not. My questions are lhf

Charlie

@JacobBlack :D

Peter Tamaroff

@JacobBlack Yes, that's why I said that.

user19161

@Tim Haha, then you should ask lhf for help.

user58512

not for me I don't even know this ito stuff

Tim

@JacobBlack ha

user19161

20:42

@PeterTamaroff I use a ballpoint pen. But I usually use a pencil for math.

user19161

@Tim I don't know. Just post your question on the site.

Tim

@JacobBlack I already. I pointed to my posts on the site.

user19161

@Tim Ah, then you should wait. Coming to this chat won't help you further much.

Tim

@JacobBlack Wait, you are good at analysis, aren't you?

user19161

@Tim No, I have forgotten all my math.

Tim

20:44

@JacobBlack How come?

Your teachers would feel sad if they hear it

user19161

@Tim Because I have not touched math for a very long time. I only answer simple questions here.

NBP

@Tim, still no answer.

Peter Tamaroff

@Tim Where?

Oh, no clue on that @TIm

I'm an underdog here.

Tim

@NBP Did is ..., you know

Charlie

Relax @tim the oompa loompas of math took the day off

user19161

20:46

@PeterTamaroff You are the boss at Spivak and Apostol!

Tim

@PeterTamaroff You are a future Field Prize winner

user58512

@JacobBlack, why dont you do advanced math now

Peter Tamaroff

@Tim I meant I'm no big one. I just googled undergod, it isn't what I meant =P!

user19161

@user58512 Because I am very sick.

Tim

@Charlie you are a mystery

user19161

20:47

@PeterTamaroff Yeah, I just realised too.

Peter Tamaroff

@Tim Why would you say that?

Tim

@PeterTamaroff well undergod is the next to god

user58512

are you going to be ok

user19161

@user58512 I don't know.

Tim

@PeterTamaroff Because Jasper Loy said so

Charlie

20:48

Yes I am @tim

user19161

How many of you have pets here?

user19161

I know robjohn and Peter has a dog.

Charlie

I have

user58512

bye

Tim

have a nice day

@JacobBlack Do you have a paid job now?

user19161

20:52

@Tim No, I am not working.

Tim

I was wondering how you make a living

user19161

@Tim Well, I have people to take care of me, I have savings and I don't spend much. QED.

Tim

@JacobBlack Life is difficult for some of us. QEd

user19161

@Tim You mean for you or me?

Tim

I know it is for me. I know it may or may not be for you

QED

user19161

20:55

@Tim It is very difficult for me, in various ways.

Charlie

Life is hard for everyone

Tim

Does "QED" mean "that's all. no more bothering"?

Dominic Michaelis

quad erat demonstrandum

user19161

@Tim My QED has no more clear meaning.

Dominic Michaelis

what we needed to prove

Tim

20:56

Mine does

user19161

@Charlie But for some, much more so than others.

Tim

Life is hard for everyone including mystery

user19161

@Tim Who is mystery?

Tim

@JacobBlack Whoever claims themselves to be

QED

Dominic Michaelis

@Tim In a good proof you know when you are done, than you don't need a QED :D

user19161

20:58

@Tim If you read my blog, you will have a small idea of what is going on, but shh...

Tim

@DominicMichaelis I like book to signal the end of proofs

So I know it is finished proven

user19161

@Tim Of course, I have deleted my blog, as I told you.

Tim

@JacobBlack Your secrets

Charlie

I use tombstone, @dominic

Tim

I am starving and need to have a meal. bye

Peter Tamaroff

20:59

@anon FML I found that with $\{e_1,e_3,e_2 \}$ You actually get $x_1x_2x_3=x_3x_2$,$x_1x_2=x_2x_1$ and $x_1x_3=x_3x_1$

Not what I wanted.

It looks similar but it is not the same.

However $Ae_1Be_3Ce_2=(A,B,C)$ in this "multiplication"

Dominic Michaelis

having 2 k repu is good

finally i don'T have to say "improved formatting" everytime

NBP

@DominicMichaelis still no answer..

Dominic Michaelis

@NBP on which question ?

NBP

1

Q: Problem with coupling (basic probability)

If I have two probability spaces : $\\\Omega_1=\{w^1_1,w^1_2,w^1_3\}$ with $P_1$ defined to be $P_1(w^1_1)=P_1(w^1_2)=P_1(w^1_3) = 1/3$ and $\Omega_2=\{w^2_1,w^2_2,w^2_3\}$ with $P_2$ defined to be $P_2(w^2_1)=P_2(w^2_2)=1/5$ , $P_2(w^2_3)=3/5.$ I am asked to find the (or a) smallest probabilit...

Charlie

@dominic congrats!

NBP

21:11

@Charlie, what for?

Dominic Michaelis

2122 reputation in 9 days :)

NBP

What's reputation?

Dominic Michaelis

the points you get if others like your questions

or your answers

NBP

nobody likes my questions appreantly

and nobody answers them ever

Dominic Michaelis

sry i don'T know anything about probality

NBP

21:13

it's the most basic probability concept

Dominic Michaelis

you got 72 reputation and someone liked your questoin already

NBP

I don't believe you haven't taken an introduction to probability theory course

Who liked my question and why

Dominic Michaelis

you have a 1 there don't you ?

it says someone voted for the question

NBP

but it doesn't get an answer, maybe one person liked it. I bet hundred have hated it

Dominic Michaelis

nope introduction to probality theory is a 4th semester course and it's my third right now

NBP

21:16

You're an undergrad?

Charlie

@DominicMichaelis here it is in the first semester

NBP

I'm only just done with my first semester and and had to take introduction to probability

oh good @Charlie so you can help me?

Dominic Michaelis

well probabily in german probability is not so important :D

Orange Harvester

@NBP You might want to learn how stackexchange works, how reputation works and in general, how public internet forums work.

NBP

How do I learn that?

MWarsi

21:18

Okay, I'm sorry to be interrupting with an elementary problem, but how do I begin to integrate 2/(a+by^2) with respect to y? Its 3 am, and my head's a mess.

Charlie

@NBP I'm not good at it , I read, but no clue

NBP

@Charlie, I trust you'll figure this out. I'll ask you again in 30 minutes

Peter Tamaroff

@MWarsi Want some help?

Dominic Michaelis

@mwarsi divide by a substitute and you should get something with arctan

MWarsi

Ah, yes, I do.

Hmm, what substitute?

Peter Tamaroff

21:20

@MWarsi Let me write this again

MWarsi

Hmm.

experimentX

Hello

Peter Tamaroff

@MWarsi You want to "homogeneize" the equation, right?

Dominic Michaelis

i would set u=\frac{\sqrt{b} y}{\sqrt{a}}

experimentX

Hi ,, can anyone help me with this quick problem

Show that {x} are open sets in X for all points x∈X, then all subsets of X are also open in X.

Peter Tamaroff

21:23

So you want $by^2$ to become a $u^2$, then you want a substitution of the form... yes, what @Dominic wrote.

Dominic Michaelis

@experimentX union of open sets are open

MWarsi

Wait wait, sorry I seem slow, but what do you mean by homogeneize the equation?

Oh, hmm.

Orange Harvester

@NBP If you trust that she can work it out in 30 minutes, why can you not in an hour?

Dominic Michaelis

@PeterTamaroff I integrated half of the bronstein that helps a lot :D

experimentX

@DominicMichaelis is it simply saying to prove that the union of {x} is open?

Dominic Michaelis

21:24

@experimentX you can't prove it

NBP

@OrangeHarvester, I'm not as clever

Dominic Michaelis

it is the definition of a topological space

experimentX

@DominicMichaelis does it mean the statement is incorrect?

MWarsi

Oh, wait wait.

Dominic Michaelis

@experimentX no it means it is a definition

MWarsi

21:25

Hey, I got it.

Ah, crap

Dominic Michaelis

you can't prove that an apple is an apple

NBP

@OrangeHarvester, what makes you think Charlie is a girl

MWarsi

u=\frac{\sqrt{b} y}{\sqrt{a}} <= Thanks for that.

Dominic Michaelis

unions of open sets must be open

@NBP cause she is one (a beatiful version )

@MWarsi i am glad i can help :)

experimentX

@DominicMichaelis knowing it ... how do i approach this problem?
Show that {x} are open sets in X for all points x∈X, then all subsets of X are also open in X.

can a point itself be open in X?

Orange Harvester

21:27

@NBP No problem. Charlie can be a guy too. I thought in order to not be sexist, I would call people randomly, some by girls name and some by boys.

Dominic Michaelis

any subset is the union of the elements

Orange Harvester

So, occasionally, I will refer to people as him and occasionally as her.

Charlie

@DominicMichaelis how do you know that, if you never saw me?

Dominic Michaelis

@experimentX yeah in the discret topology all points (and so all subset) are open

@Charlie i don't need to see things to know they are true :)

NBP

@Charlie, are you from Israel? You got a hebrew letter next to your name

experimentX

21:28

@DominicMichaelis i see ... thank you very much for you time, could you suggest some article for reading?

Orange Harvester

@NBP Yes.

Dominic Michaelis

@experimentX nope sry i didn't take a topology lecture till now

NBP

@OrangeHarvester, Yes to what question?

experimentX

ow ... still thank you very much for your time

Orange Harvester

@NBP Yes. He is from Israel.

NBP

21:32

@OrangeHarvester, Charlie is not a common Israeli name so I don't think it's true

Orange Harvester

@NBP Neither is Orange Harvester a common people name, so may be I am not a person, but actually a fruit picker.

NBP

@OrangeHarvester, are you trolling me?

Peter Tamaroff

@anon OK, $e_3,e_2,e_1$ in that order fulfill the equations.

Orange Harvester

@NBP No. (I am completely serious, being a mathematician and all, humor is below me.)

NBP

@OrangeHarvester are you saying that fruit pickers are not persons?

Orange Harvester

21:36

@NBP Fruit Picker is a mechanical tool used to pick fruits (as shown in my profile photo). They cannot be persons I think.

NBP

@OrangeHarvester, a person can't pick fruits?

Orange Harvester

@NBP He can, but then he would not look like my profile pic, which is what I referred to when I said, I am a fruit picker.

NBP

@OrangeHarvester, then you're trolling me. Or you're insulting me. A Fruit Picker as you describe it would not be sentient and chat with me like this.

Orange Harvester

@NBP I can if I am clever

NBP

As afortementioned you don't have intelligence, you're not sentient so you can't be clever (or dumb).

I dislike your trolling. Please cease it

Orange Harvester

21:46

Point Noted. Now, somethings for you:
1. People can use pseudonames on this site (though some may not). The objective is to protect privacy.
2. This site is a volunteer effort, people live in all over the world, did may be in his REM sleep right now.
3. It is dangerous to give out phone numbers on internet to strangers, do not do it yourself.
4. People answer questions in their own time. (Volunteer work.) They may or may not choose to answer further than they have already done. Trying to ping them multiple times is an invasion of their privacy.

NBP

@OrangeHarvester, I'm sorry. I guess you're right (except for the phone numbers over the internet, how exactly is that dangerous?)

@OrangeHarvester, it still feels like you're trolling me.

Orange Harvester

@NBP Now, I am not trolling. I was initially before, after being pissed off at your efforts to get phone numbers. But now I am not.

NBP

@OrangeHarvester, I believe you. This list seems of more serious nature - however why were you pissed at me for trying to get phone numbers?

Orange Harvester

@NBP List is not of serious nature. We make jokes around here too.

I was pissed off because you were treating this list like some kind of support center where you expect people to respond to you in real time.

NBP

@OrangeHarvester, I'm not expecting anything, but my question is pretty basic and I've seen much more complicated question get answered in no time.

Orange Harvester

21:55

@NBP As I said, your question has to appeal to people. Most of the time, if the question is very easy, people provide only hints in order for the student to work stuff out themselves. By the time you have asked a counter question to the hint, they might have shut down their computer and gone to sleep.

NBP

@OrangeHarvester you just answered yourself why I would want their phone number.

@OrangeHarvester, how would they know that I still need help if they shut off their machine?

Dominic Michaelis

@GitGud what is your picture about? It reminds me on Kentucky fried chicken (i guess it's only the color)

Orange Harvester

@NBP Have you thought they might not want to help over phone? That for some, the activity is purely an internet activity?

NBP

@OrangeHarvester, they can just mention it and I'll apologize and hang up

Orange Harvester

@NBP but why? what if they do not want to be identified by their real credentials on the website? (pseudonyms)

Charlie

21:58

@DominicMichaelis fried chicken is so damn good

Transcript for

$Mathematics$ Mathematics