D**o
发帖数: 2653 | 1 注意作者 \author{YHBKJ}
Atiyah-Bott Localization 1
2012-09-05 09:24:19
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\begin{document}
\title{\textbf{\Huge{Atiyah-Bott Localization 1}}}\author{YHBKJ}\date{}\
maketitle
\begin{ab... 阅读全帖 |
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h*h
发帖数: 27852 | 2 【 以下文字转载自 Military 讨论区 】
发信人: threeheart (氷), 信区: Military
标 题: 电工科普：张汤姆素数对证明原理
发信站: BBS 未名空间站 (Sun Feb 1 23:37:08 2015, 美东)
昨天贴了个关于张汤姆证明的帖子，引来几个装逼傻叉的质疑，怀疑老子装逼看不懂，
所以现在我觉得有必要科普一下张汤姆的证明原理。这里强调是原理，不是详细过程，
但这并非是因为我没看懂过程，而是因为张汤姆的文章有56页，要解释清楚每个证明大
概需要两倍的56页。而且，这是个需要大量函数和公式的证明，没有公式将极其难以说
清楚，而本版帖子是没法打公式的。所以，你要是看懂了没有公式的本贴，就知道叔是
如何的牛逼且又是如何的低调，而且也会发现你是多么的牛逼，能看懂张汤姆的素数对
是咋回事。
本贴分两部分，第一部分是给我一样的数论钓丝门外汉看的，第二部分是张汤姆文章导
读。重点是第一部分，如果你看懂了第一部分，那么看第二部分应该象上厕所一样的容
易。而如果你看懂了第二部分，自然会去读张汤姆的原文，那时也就没我什么事了。
不过还是有几个前提条件，一，你... 阅读全帖 |
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l****a
发帖数: 86 | 3 non reflecting:
Simply put: p=0
or more precisely: rho*c termination: Z=rho*c
Axisymmetrical bc: Vt=0 instead of Vn... |
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r********r
发帖数: 352 | 4 给你做讲座的不会是我们班出去的泰国妹吧。呵呵，听着象。
midyear我们还聚过，今年轮到她来面试别人了。她是我们那届的rho chi主席，我们上
上届的rho chi主席也是去了Rutgers fellow.
我觉得 industry 挺好的，如果年轻，单身，我会考虑走这条路。 |
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t*****e
发帖数: 133 | 5 各位大牛，请帮忙看看这个作业题，谢谢。
The following method is used to measure the molecular weight of very heavy
molecules. A liquid containing the molecules is spun rapidly in a centrifuge
, which establishes a variation in the density of the liquid. The density is
measured, such as by absorption of light, to determine the molecular weight
. Assign a fictitious "centrifugal" force to act on the molecules and show
that the density varies as
rho(molecule)=rho(liquid)exp(mw^2x^2/2kT), where w is the angular velocit |
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V****n
发帖数: 651 | 6 I think you made a couple of mistakes. The unit of thermo conductivity is W/
m-K, your equation fails to balance the unit.
The transient heat conduction equation is
k*(d2T/dx2+d2T/dy2+d2T/dz2)+Q' = rho*c*dT/dt (figive my non-rigorous
notations here)
where k is the heat conduction coef., Q' is the internal heat generated per
unit volume per unit time,
rho is density and c is specific heat (for solid Cv and Cp are about the
same)
When a person dies Q'=0. You've already calculated the right hand si |
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t**********m
发帖数: 205 | 8 探索星系的捷径
A Shortcut to Galaxy Exploration
（请帮忙修改中文，并翻译成英文）
1. 问苍天情为何物？
有人类的历史以来，人类就不断地探索自然，扩展了解自然的疆界。哥伦布发现新大陆
就是最好的例子。人类探索自然的勇气是从哪儿来的呢？来自人类情感的力量。那么，
情感是什么东西呢？这是千万年来，文学家探索的主题。在有一些文学家的眼中，物理
学家是没有情感的冷血动物。我就是一个物理学家。但是，我一点也不埋怨这些文学家
。虽然物理学家在自然界的探索中做出了伟大的贡献，但是，物理学家从来就没有给出
情感的物理定义是什么，也没有找到自然界蕴含情感的丝毫证据。所以，虽然人类知道
自己的生存发展跟自然环境是密不可分的，但是，很少有人类表达出对自然环境感谢的
情感。在很多人的眼中，自然界是死亡无情的物质世界。中国有一句古语，叫做“天若
有情天亦老”。因为几乎所有人类相信天是不老的，所以，认为苍天是没有情感的，就
不足为奇了。我提出了一个宇宙生长衰老的模型。虽然这个模型及其简单，能解释大多
数重要的宇宙观测结果，但是，遭到冷落是它的必然命运。
但是，我的关于星系的模型，... 阅读全帖 |
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t**********m
发帖数: 205 | 9 如何宣传这么重要的论文？？
http://vixra.org/pdf/1102.0035v1.pdf
http://vixra.org/author/Jin_He
The Nature's Selection of Cubic Roots
The English naturalist Charles Darwin established that all species of life
have descended over time from common ancestry, and proposed the scientific
theory that this branching pattern of evolution resulted from a process that
he called natural selection. In fact, Darwin theory dealt with the
evolutional phenomena of the biosphere, not its origins. Further more, there
exist the... 阅读全帖 |
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z****0
发帖数: 1351 | 10 例如球上有一点坐标（rho,theta,phi）,整个球随机转动theta1,phi1的角度，这个点
得到一个新的坐标（rho,theta',phi'），请问有没有类似绕XYZ转动的矩阵存在？谢谢 |
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r**a
发帖数: 536 | 11 what r u talking about? See your last eq.(eq.4), first you'd better not
raise $\mu$ to $\rho$ at this moment and leave $g^{\mu\rho}$ there. And
notice that $\mu, \nu$ are aniti-symmetric. Then change the partial
derivative to the covariant derivative. And then... |
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S*******s
发帖数: 13043 | 12 自己抛个砖吧
考虑风吹墙，正面受力
mv=ft
rho*S*t*v=f*t
f/S=rho*v |
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c******s
发帖数: 90 | 13 Please see this link below.
http://www.noise.cz/sbra/sibram02/2-Ses/Fegan.htm
In this paper, the author present a way to generated correlated uniform R.V.
Another result you may be able to use is:
If X and Y are bivariate-normal with correlation rho,
Let Ux=normcdf(X) and Uy=normcdf(Y), then
Ux and Uy are bivariate-uniform with correlation
(6/pi)*arcsin(rho/2). |
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G*********o
发帖数: 2045 | 14 1. divide and conquer，在2^n的方块中心处摆一个L片，不overlap有空的quarter，
这样就recurse成四个2^(n-1)的方块，each with one empty spot
2. 想不出来
3. 赌head，概率是2/3
4. 假设已经产生了两个indep的standard normal, w1 and w2，那么令n1 = w1, n2 =
rho*w1 + sqrt(1 - rho^2)*w2
某号称super selective的公司的onsite，去之前就没报什么希望，知道我要去面这家
公司的朋友回应都清一色的是“啊，放
轻松，就当长长经验值吧”。最后面了三个人，每个人大概一个小时，还想着有第四个
人的时候HR就进来了，俺其实就知道
没戏了。过了两天正式被拒。个人觉得主要是被中间那个还是本科同校同系的大师兄活
活问死了，不过我确实也编程不
行，去之前就说清楚了，问之前也说清楚了，可是他还是继续问哈。当然，俺恐怕也没
他们需要的那么“聪明”咯。
anyway，贡献其中几个brainteaser吧。
1. chess board，任意空出一 |
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z****e
发帖数: 2024 | 15 in this case, the result is:
(2*sigma_x^2-3*rho*sigma_x*sigma_y+sigma_y^2)/
(4*sigma_x^2-4*rho*sigma_x*sigma_y+sigma_y^2)*
(2X-Y)
The denominator will be canceled out if you expand the pdf of 2X-Y. |
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a**m
发帖数: 102 | 16 There are two stocks with prices S_1 and S_2 drived by different Brownian
motions. The stocks have the same drift, but different volatility sigma_1=0.
2, and sigma=0.3. Moreover, the correlation of two stocks is rho=0.5. What
combination of two stocks has the least risk?
I actually did not fully understand this question. My guess is the
correlation rho=0.5 means that dW_1*dW_2 = 0.5 dt. And the risk means the
variance of the combination. Any comments is welcome. Thanks. |
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s*******r
发帖数: 63 | 17 不能记得很清楚了，说个大概吧。应该是很基本的，但是对于我物理背景困难了一点。
1. a random variable, W, follows Brownian motion, W^n is a martingale, what'
re values of n?
2. three random variables have the same pairwise correlation function, \rho,
what's rho?
3. a stock, 10$/share, a year later, $12 with prob 60%, $8 with prob 40%,
what's the price of a call option? |
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r*******s
发帖数: 303 | 18
what'
d(w^n) = drift dt + xxx dw,
drift =0 ==> n=0, or 1
rho,
不知道， 如果三个都一样，就是 \rho =1
如果三个都在二维平面上，就是-1/2
其他。。。
depend on interest rate, probability measure, strike.
exp(-rt)*E(max(S(T)-K)) |
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l******y
发帖数: 507 | 19 3 RVs have same pairwise correlation rho, what could rho be? |
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s***e
发帖数: 267 | 20 Generalization to n RVs, the range of rho will be
rho >= - 1/(n-1) |
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c****2
发帖数: 31 | 21 Use Triangle. The COS(Angel)= rho.
So Cos(A)=Cos(B)=Cos(C)
A=B=C=60 degree. So Rho=1/2 |
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W*****k
发帖数: 158 | 22 假设X_1,...,X_n的variance都是1
考虑 X_1+...+X_n的variance
= n + n(n-1)rho >=0
所以rho>= -1/(n-1) |
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h**o
发帖数: 78 | 23 Assume x,y,z have unit variance, then
var(x+y+z) = 3 + 6*rho >= 0, so rho >= -1/2 |
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S*******r
发帖数: 11017 | 24 我的功力不足子弹牙十分之一，所以力所能及地解答一下。
有关第2）题
For antithetic variables, we pick 2 different but correlated sequences of iid N(0,1) or U[0,1] to run the MC simulation--let's say U and U' where U + U'= 1 so rho(U,U')=-1. The estimated price is C1,C2,..., Cn so without variance reduction, its std err is var(C)/n; now we use U to estimate C, and use U' to estimate C', and we take the average (C+C')/2 as the final estimate. Here the new std err is Var[(C+C')/2]=.25*Var(C+C')=.5*Var(C)[1+rho(C,C')] which is small |
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z****i
发帖数: 406 | 25 多谢大牛，看懂了。
你们真牛，唉。。。 要补的东西真多。
Thank you so much!!!
iid N(0,1) or U[0,1] to run the MC simulation--let's say U and U' where U +
U'= 1 so rho(U,U')=-1. The estimated price is C1,C2,..., Cn so without
variance reduction, its std err is var(C)/n; now we use U to estimate C, and
use U' to estimate C', and we take the average (C+C')/2 as the final
estimate. Here the new std err is Var[(C+C')/2]=.25*Var(C+C')=.5*Var(C)[1+
rho(C,C')] which is smaller than Var(C).
/n; Now let's plug in one more sequence |
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n******r
发帖数: 1247 | 26 Is that P(max(X,Y)
Then use Y|X=x is N(/rho*x,1-/rho^2) and x
Finally integrate x from -inf to inf? |
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b******e
发帖数: 118 | 28 X = rho * U + sqrt(1-rho^2)*V, right?
For this problem,X = 1/sqrt(2)*(U+V), not (U-V)??
But the final answer is same, 0.25. |
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l*********t
发帖数: 89 | 29 请各位兄弟路过此题拔刀相助。
本题我有一定的思路但最终结果不明朗。
题目：
You long a straddle(ie. long a call, long a put). When the risk-free rate
goes up. what happens to your position?
我求的是Greeks里的rho, 即option value对risk-free rate的偏导，最后此portfolio
的rho的表达式是 K*(T-t)*exp(-r(T-t))*(2N(d2)-1）
不过此式对r求导始终会留下N(d2)项，这样risk-free rate 总在normal distribution
里，不方便分析。
请诸位大侠指教，先谢了~ |
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l*******1
发帖数: 113 | 30 1.
exp(2*mu1+2*mu2+var1+var2+2*rho*sd1*sd2) * )(exp(var1+var2+2*rho*sd1*sd2)-1)
2. T^3/3 |
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a****5
发帖数: 2 | 31 Reference:
Here are the books I used for preparation. All the commons are just my
opinion.
1. "A Practical Guide to Quantitative Finance Interviews": You should be
fine with most of the standard
BT/Probability/Math/Option pricing questions if you truly UNDERSTAND every
part of the book.
2. "C++ Primer": It is too lengthy and is full of details. But it is very
comprehensive and you can find
everything there (before or after you are asked the questions :) )
3. "Effective C++": The first 10 ~ 20 it... 阅读全帖 |
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f*******g
发帖数: 377 | 32 尽管写的是corr(X, Y)=\rho
但这个rho应该指的就是corr(lnX, lnY)
要不然不太好办
(lnX, lnY) is a bivariate normal? Anyone can help? Thanks! |
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d********t
发帖数: 9628 | 33
那传统方法只要产生两个随机数U,V，
X=U,
Y=rho*U+sqrt(1-rho^2)*V |
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k*****y
发帖数: 744 | 34 For Prob 4, consider the plane region defined by X>0 and X+Y>0，it is easy to see that the answer is 3/8.
For Prob 3, -1/3 is necessarily a lower bound for \rho to get a semi-
definite matrix, since (1+3\rho) is the eigenvalue for (1,1,1,1)^T.
Consider a regular tetrahedron inscribed in S^2. Any angle between two rays
from the center through a vertex is arccos(-1/3). This model can be realized
by a joinly normal distribution.
It can be generalized to the case of n+1. Consider a regular (n+1)-gon，... 阅读全帖 |
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i****b
发帖数: 52 | 35 请问各问， SABR model
dR_(t+1)=R_t^\beta \sigma_t dW
d(log\sigma_t))=\nv dZ
Z and W are brownie motions and =\rho
\sigma_t are latent volatilities, \beta, \nv, \rho are real parameters. How
should I estimate the path of \sigma's in this model?
多谢多谢～～ |
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j******n
发帖数: 91 | 36 Assuming x - N(mu_x, sigma_x), y - N(mu_y, sigma_y), rho(x, y)=rho. Given z
= x+y (z is known), what is E(X|X+Y=z)? |
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k**y
发帖数: 920 | 37 sigma_x和sigma_y是std对吧？
let Y'=X+Y
then EY'=mu_x+mu_y
std(Y')=sqrt(varX+varY+2rho*sigma_x*sigm_y)
Cov(X,Y')=Cov(X,X+Y)=varX+Cov(X,Y)=sigma_x^2+rho*sigma_x*simga_y
根据Normal Dist条件分布的公式
E(X|Y'=z) = mu_x + sigma_x/std(Y')*corr(X,Y')*(z-EY')
= mu_x + Cov(X,Y')/std(Y')^2 *(z-mu_x-my_y)
= mu_x + (sigma_x^2+rho*sigma_x*sigma_y)/(sigma_x^2+sigma_y^2+2rho
*sigma_x*sigma_y *(z-mu_x_mu_y)
z |
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W**********r
发帖数: 68 | 38 5. Suppose you have bought a July ITM call and sold an August ATM put.
What would be your delta in this position? Once you hedged out your delta
what are the following greeks:
-Gamma
-Vega
-Rho
-Theta
这个我觉得是long Gamma，short Vega， long Rho， paying Theta
6. Suppose you know the following information about a market:
- Future is at 66
- 70 strike straddle is trading at 27
- 50-60 put spread is at 2.5
- 50-60-70 put fly is at .2
- Assume volatility is constant across strikes
Using the prices given an... 阅读全帖 |
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l********g
发帖数: 18 | 39 the delta should be positive，delta(ITM)>0.5, ATM put =0.5. As for gamma
should be negative, normally it is concentrate on strike, ATM gamma> ITM
gamma. As for vega, it is spread, so you got a vega negative. Rho ,you got
the liquid, so you got a short rho. As for theta, you have trade off, so
positive theta |
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e*******8
发帖数: 6 | 40 5. Suppose you have bought a July ITM call and sold an August ATM put.
What would be your delta in this position? Once you hedged out your delta
what are the following greeks:
-Gamma
-Vega
-Rho
-Theta
Answer: Positive Delta. It is obvious.
- For Gamma, I think it is hard to say, it depends on how deep the July call
is ITM. It is true that Gamma is centered around the strike, but for the
same strike, the Gamma for shorter maturity options is more skewed, which
may lead to a situation that the gam... 阅读全帖 |
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s***e
发帖数: 911 | 41
顶点位置设为{R_i}(i=0,..,N), 那么第kth个线段矢量定义为
r_i=R_{i}-R_{i-1},i=1,...,N
每个线段的空间分布(长度固定为b)完全随即:
\rho(r)=(1/4*pi*b^2)*\Delta(|r|-b)
这个纯粹是空间取向分布, 各个segment独立. 所以联合分布就是:
\PHI({r_{i}))=Product[\rho(r_i),i=1,N]
首位距离矢量:
R=R_{N}-R_0=Sum[r_{i},i=1,N]
R作为{r_i}的函数, 它的分布从联合分布\PHI({r_{i}))求得:
\phi(R)=Integrate[\delta(R-Sum[r_{i},i=1,N])*\PHI({r_{i})) dr1dr2dr3...]
对\delta函数作台劳展开,并且采用球坐标得到:
\phi(R)=1/(2 Pi)^3 Integrate[Exp[i k.R]*(sinkb/kb)^N,dk]
对大N, 可以把(sinkb/kb)^N展开,就得到一个高斯积分.最后计算得分布是高斯分别:
\phi(R)=(3/2*Pi*Nb^2) |
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c**********g
发帖数: 222 | 42 >>>> this is wrong. what offset the gravity of the sun is the gas pressure
( acturally, it is the gradient of the gas pressure). The pressure is positive.
when we mean that the pressure is positive, we mean that P1,P2 and P3 the trace
of the energy-monentum tensor (\rho+P1+P2+P3) is positive. Here, \rho is the energy
density
>>> Also, in NS, gravity is balanced by the gradient of the neutron denenerate
pressure. Again, this pressure itself is positive. |
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a**u
发帖数: 99 | 43 这个题目真要考虑,还是怪麻烦的.
一边升还要一边扩张.
先搞一个稳衡近似叭.
浮力F=RHO*V. V是体积.
PV=const.
P=RHO*g*H
初始条件,v=0,V=V0.v是速度.
气泡的质量为m,没有重量这条可以理解为重力可忽略不计.
然后根据牛顿定理,不难写出加速度乐,
不知道是不是简化的太多乐.是不是泥要得模型. |
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r*f
发帖数: 731 | 44 还有一个，再帮帮我吧
write the expression for the kinetic energy of a fluid
flow occupying a volume V by a surface S. If the flow is
irrotational and incompressible prove that the kinetic
energy is given by
{\rho}/2*{\intergral_s{\phi*{d{\phi}/dn}dA}
where \rho is density, \phi is the velocity potential.
d in d{\phi}/dn means partial differential.
//bow again |
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h****l
发帖数: 7290 | 45
sonic boom 中文叫音爆，是物体以超音速运动（或气流以超音速吹来）时
发出的一种象打雷一样的声音。其实也就是激波和其他物体作用的时候产生
的声音，因为激波前后压力差别很大，而声音其实就是压力脉动，所以，激
波是一种很强的声源。你再往下问，我就不知道咧......
sonic throat 应该是指雍塞的现象，气体在亚音速运动时，密度随速度的变化
不大，而质量流量为rho*A*V，其中rho为密度，A为截面积，V为速度，所以
气体在管道内流动，管子变细，气体就加速。而超音速的情况完全不同，密度
随流速增加而快速下降，所以管道必须扩张，流速才增加。这样就会出现一个
现象，一个变截面管子，在入口加很大的压力，气流在管子最细的地方肯定是
音速，入口怎么再加压，流速也不再增加。这个这个喉道就叫sonic throat。 |
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m*******s
发帖数: 469 | 46 http://www.rhoworld.com/rho/career-center/opportunities#jobid_359
Biostatistics - Chapel Hill, NC
(Job Code: 00359) - Apply...
Responsibilities:
As a biostatistician at Rho, you will participate in multiple clinical
trial projects. Under the direction of a lead biostatistician, you will:
Prepare analysis plans and specifications for analysis data sets and
data displays (tables & graphs)
Analyze clinical trial data and interpret the results, either in a
statistical report or as part of a clinical |
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m*******s
发帖数: 469 | 47 http://www.rhoworld.com/rho/career-center/opportunities#jobid_361
Biostatistics - Chapel Hill, NC
(Job Code: 00361) - Apply...
Responsibilities:
As a biostatistician at Rho, you will participate in multiple clinical
trial projects. Under the direction of a lead biostatistician, you will:
Prepare analysis plans and specifications for analysis data sets and
data displays (tables & graphs)
Analyze clinical trial data and interpret the results, either in a
statistical report or as part of a clinical |
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o****o
发帖数: 8077 | 48 if assuming a linear normal model
A=\beta B + e; e~N(0, sigma)
note there is no intercept
the after some algebra, it can be shown that \hat{\beta}=\rho(A, B)*std(A)/
std(B)
A ~= \rho(A, B) * sqrt( var(A)/var(B)) * B
does this work? |
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c******n
发帖数: 380 | 49
A
From rho=1, I can only tell that A and B have perfectly positive linear
relationship. Could you be more specific about why rho=1 leads to that
when A occurs, B must occurs? Thanks |
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M******8
发帖数: 22 | 50 遇到点问题，问问版上的牛牛们～～
我在算two sample correlation的时候，用了Kendall's tau and Spearman's rho.
但是最后算出来的结果却是不一样的。Kendall's tau的结果是 p<0.05,但是Spearman'
s rho的p >0.05。这是为什么呢？
谢谢啦～～ |
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