/sci/ - Science & Math

OP = FAGGOT

QED

the volume of a pizza with radius z and height a

is pi*z*z*a

crazy huh?

>>3988675

http://en.wikipedia.org/wiki/Borwein_integral

>>3988675
I...don't get it

>>3988711
integral zee squared dee zee
from one to the cube root of three
times the cosine
of three pi over nine
is the log of the cube root of e

>>3988711
cos pi/3 =1/2

the integral is 1-1/3=2/3

so it's all equal to 1/3

get it?

>>3988696
har dee harr harr

All time favorite. I don't know what it means, it's just from the poster of Information Theory and Applications workshop 2009 (low res version here: http://ita.ucsd.edu/workshop/09/images/home_bg.jpg ) where the authors had to submit a "cool" formula for the poster of the workshop. Mine wasn't quite as cool :/

<div class="math">\hat{\omega}\mathbb{D}(\mathcal{P},\mathcal{F},R)\leq \sup_{\alpha>0} ~~ \inf_{\delta>0}~~ \sup_{P'\in\mathcal{M}(\mathcal{Y})} ~~ \inf_{Q_{U|Y}: ~I(P'\times Q_{U|Y})\leq R+\alpha} ~~ \sup_{P\in\mathcal{P}: ~||P_Y-P'||_V\leq \delta} ~~ \mathbb{E}_{P\times Q_{U|Y}} ||\delta_{X,U}-P||_{\mathcal{F}}</div>

Awesome!

(actually here's the full res poster in PDF: ita.ucsd.edu/workshop/09/files/ita2009.pdf )

>>3988743
yeah I got 1/3...I don't get what's funny

>>3988804
It's a limerick. Admittedly not the peak of humor, but such is math.

>>3988790
And that was me after dropping my tripcode to troll other boards... Ah...

>>3988832
Is it long formula time?
<div class="math">Z=\prod_{k_<}\int\mathrm ds_{k_<}\exp\left(hs_0-\frac12\int_{k_<}k_<^2s_{k_<}s_{-k_<}-\omega\int_{k_<k'_&lt
;}^{|k+k'|<b^{-1}\Lambda}s_{k_<}s_{k'_<}s_{-k_<-k'_<}\prod_{k_>}
\int\mathrm ds_{k_>}\exp\left(-\frac12\int_{k_>}k_>^2s_{k_>}s_{-k_>}\right)\exp\left(-2\omega\int
_{k'_<}s_{k'_<}\int_{k_>}s_{k_>}s_{-k_>-k'_<}-\omega\int_{k_>k'_<}s_{k_>}
s_{k'_>}s_{-k_>-k'_>}\right)\right)</div>

>>3988885
Yeah, but mine has "sup inf sup inf sup"! Can't get much cooler! Though, yours is not only longer, but also deeper in terms of operation tree... Damn, a product of integral of exp of sum of something times integral of something times product of integral of product of something times exp of product of constant times product of integral of product of something, I count ~17 levels, what the hell...

>>3988914
I agree that yours is way cooler. (Plus my thing wasn't a formula to be used but an intermediate step in renormalization, so it doesn't really count anyway)
Is there some way of understanding it? "lim"-wise?

>>3988914
I agree that yours is way cooler. (Plus my thing wasn't a formula to be used but an intermediate step in renormalization, so it doesn't really count anyway)
Is there some way of understanding it? "min/max"-wise?

8=D

>>3988920
Dunno. I don't have the proceedings so I can't check the paper it's from. I can see if google gives something. It should be on ieeexplore or maybe on ucsd's website.

I'll check.

>>3988948
Yup, found it:
http://ita.ucsd.edu/workshop/09/files/paper/paper_1442.pdf

"Achievability Results for Learning Under
Communication Constraints"

Abstract:
The problem of statistical learning is to construct
an accurate predictor of a random variable as a function of a correlated random variable on the basis of an i.i.d. training sample from their joint distribution. Allowable predictors are
constrained to lie in some specified class, and the goal is to approach asymptotically the performance of the best predictor
in the class. We consider two settings in which the learning agent only has access to rate-limited descriptions of the training
data, and present information-theoretic bounds on the predictor performance achievable in the presence of these communication
constraints. Our proofs do not assume any separation structure between compression and learning and rely on a new class
of operational criteria specifically tailored to joint design of encoders and learning algorithms in rate-constrained settings.
These operational criteria naturally lead to a learning-theoretic generalization of the rate-distortion function introduced recently
by Kramer and Savari in the context of rate-constrained communication of probability distributions.

<span class="math">\int_{10}^{13} 2x dx[/spoiler]

<span class="math"> b_4 i\sqrt{u} \frac{ru}{18}[/spoiler]

/sci/: TN5, Marion Bartoli, and Josef's treehouse hangout

>>3988965
Oh wow. And it's not like the rest of the paper is beautiful, the formulas are only shorter.

>>3988990
Yeah I'm not sure if it's interesting at all. Just like "i have these parameters and my function is obviously increasing with this 2 and decreasing with this 3". I wouldn't be surprised if most of the infs and sups could commute, making the formula far less cool.

I doubt the paper is worth reading just to find out, though.

>>3988993
It's actually pretty sad because I post as anon half the time.

>>3989002
Frustrated magnetic correlations in fermionic systems are the subject of current and promising research in modern condensed-matter theory. Generalized (fermionic) spin glass models and certain Hubbard models form two model classes for theoretical investigations of these phenomena in disordered and clean systems, respectively. The coupling to a particle reservoir allows to control important parameters such asfermion concentration or effective spin density by means of a chemical potential. The important experimental tool of doping often leads to quantum phase transitions (QPT), metal-insulator transitions, or magnetic phase transitions being prominent and standard examples thereof. The chemical potential <span class="math">\mu[/spoiler] or, alternatively, the fermion filling <span class="math">\nu[/spoiler]) is thus a relevant variable for the phase diagram. In quantum spin glass theory, a well-known model showing a QPT as the effect of a disordering transverse field <span class="math">h_\perp[/spoiler] is the transverse field Ising model; in the present paper, the chemical potential <span class="math">\mu[/spoiler] is considered instead, playing the role of a generalized transverse field: <span class="math">\mu[/spoiler] couples to the charge, while <span class="math">h_\perp[/spoiler] couples to transverse spin degrees of freedom. Since particle number operators and Ising spin operators commute, the chemical potential does not generate quantum spin dynamics. On the other hand, single fermion operators do not commute with the spin interaction and hence quantum dynamics always exists in the fermionic spin glass models. This kind of dynamical behavior is reflected for example in the fermion propagator and its spectral density determines the band structure.

Secant

>>3989027
I understand such a little ratio of the technical terms in that abstract that I had to google it to see if you were trolling me. Also, stopped reading at "chemical".

>>3989042
I never joke.
http://prb.aps.org/abstract/PRB/v62/i13/p9030_1

>>3989036

I don't get it

Ein paar gute Mathe paper titel:

>Hodge's general conjecture is false for trivial reasons
(I love him)
>You Could Have Invented Spectral Sequences
>Can one hear the shape of a drum?
(klassiker)
>A minus sign that used to annoy me but now I know why it is there
>How not to prove the Poincare Conjecture
>Ramanujan's association with radicals in India
>Is the null-graph a pointless concept?
>Everybody knows what a Hopf algebra is
>On O_n
>Free rings and their relations
>Six standard deviations suffice.
>The importance of being straight
>The homotopy category is a homotopy category
>Division by three
>A Group of Order 8,315,553,613,086,720,000
>Holey Sheets
>On groups of order one.
>K-Theory and Reality
>The Joy of Sets.
>Applied Mathematics is Bad Mathematics

>>3989109
Nice. If these are really interesting papers, I love the guy too. Actually, if they're parody papers like the "complexity of songs" and such, I might love him even much.

r d rr is the best one.

also the nerd's equation (nernst eqation)

>>3989131
these are all papers by different people. The first one is by Grothendieck
>dat bio
http://en.wikipedia.org/wiki/Grothendieck

"I've had the chance, in the world of mathematics, to meet quite a number of 
people, both among my elders and amoung young people in my general age 
group, who were much more brilliant, much more "gifted" than I was. I 
admired the facility with which they picked up, as if at play, new ideas, 
juggling them as if familiar with them from the cradle -- while for myself 
I felt clumsy, even oafish, wandering painfully up an arduous track, like a 
dumb ox faced with an amorphous mountain of things I had to learn (so I was 
assured), things I felt incapable of understanding the essentials or 
following through to the end. Indeed, there was little about me that 
identified the kind of bright student who wins at prestigious competitions 
or assimilates, almost by sleight of hand, the most forbidding subjects. 
In fact, most of these comrades who I gauged to be more brilliant than I 
have gone on to become distinguished mathematicians. Still, from the 
perspective of thirty or thirty-five years, I can state that their imprint 
upon the mathematics of our time has not been very profound. They've all 
done things, often beautiful things, in a context that was already set out 
before them, which they had no inclination to disturb. Without being aware 
of it, they've remained prisoners of those invisible and despotic circles 
which delimit the universe of a certain milieu in a given era. To have 
broken these bounds they would have had to rediscover in themselves that 
capability which was their birthright, as it was mine: the capacity to be 
alone."

>>3989149
I just read, googling about the null graph paper:
>According to Brendan McKay (2002), it is an exception to so many things that the community (or most of it) has decided that the only good null graph is a dead null graph.
:-)

>The culture's growth curve plateaued at the x axis.
When discussing the effect of certain compounds on a bacterial culture. ... ie., it died.

Division by Three... fuck yeah Conway.

A little nighttime reading.

>>3989179
That's a 35 pages paper for a result that looks so fucking trivial... I must be missing something there.

The result is obvious for A and B finite, so I guess we're talking about infinite sets here. But then... what? <span class="math">A\asymp 3\times A[/spoiler], right?

Forgive me, it's late, am I saying stupid things?

>>3989193
Ok, I read two more paragraphs, and he answered both my questions. Never mind... :p

>>3989149
Wow.

>>3989225
Wow.?

Well yes.

>>3988733
how the fuck would I know to read it in that particular order.

dx sounds like dicks

why is 6 afraid of 7?

789

>>3989455

Integral of 1/cabin

thats all I got

>>3989600
I lol'd