User id0 - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T19:56:59Z http://mathoverflow.net/feeds/user/20473 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/103935/brownian-bridge-in-two-variables Brownian bridge in two variables? id0 2012-08-04T11:29:16Z 2012-08-04T14:43:42Z <p>Hi</p> <p>I know about the Brownian bridge, for example $B_t = W_t - tW(1)$. Is it possible to create it in 2D? ie, to have a 2D Brownian motion, which constitutes a surface, and have it return to 0 when the distance (according to some metric) from the center is equal to some constant?</p> <p>For example, to have an image which is a Brownian motion realization and have it conditioned as equal to 0 on the unit circle.</p> <p>Thanks.</p> http://mathoverflow.net/questions/92494/expected-value-of-partial-sum-of-iids-given-the-full-sum expected value of partial sum of iids given the full sum id0 2012-03-28T19:39:10Z 2012-03-28T20:22:35Z <p>Hi </p> <p>I need to calculate $ES_n|S_m$ for $S_i=\sum_i X_i$ and $X_i$ are some iid (not a specific distribution), and $m>n$ . ie, calculate the expected value of a partial sum given the entire sum. I think it's just the partial sum, $\frac{n}{m}\cdot S_m$ but I don't know how to prove it. Trying to explicitly use the expectation definition didn't go anywhere.</p> <p>Thanks</p> <p> The best I could do is symmetry - because if I look at one $EX_i|S_n$ it should be equal for each i, then they should be the same. But it's not really a proof...</p> http://mathoverflow.net/questions/92451/given-ft-sum-k-c-k-exp2-pi-i-w-k-t-noise-need-to-estimate-c-k-and-w-k/92498#92498 Answer by id0 for Given f(t) = \sum_k C_k exp(2 pi i w_k t ) + noise. Need to estimate C_k and w_k . id0 2012-03-28T20:02:45Z 2012-03-28T20:02:45Z <p>You have what's called a 'predictable' process (sum of shifted diracs) and a simple regular process (white noise in this case). You can just average out signal as much as you like, the harmonies will stay the same and the noise will diminish. You can actually get as low a noise as you like. </p> <p>If you just want to threshold the coefficients, you can try it by seeing the FFT (white noise has a constant frequency response and the exponents will be peaks), you will immediately see the threshold. You can also calculate it via the power (or variance) of the noise, but this also relies on you knowing the amplitude of the C's.</p> http://mathoverflow.net/questions/85325/optimization-of-a-matrix-with-an-objective-function-for-ml Optimization of a matrix with an objective function (for ML) id0 2012-01-10T10:50:53Z 2012-01-10T11:36:26Z <p>Hi.</p> <p>I need to do max. likelihood for an objective likelihood function L (minimize it), and the target is a matrix. ie:</p> <p>$$min_KL(K)$$ </p> <p>For example: K is, let's say, of size 3x3 and with initial value of ones ($k_{i,j}=1∀i,j$). L is $L=∥\nabla(K)∥$ or $L=∥K∥^{1.1}$.</p> <p>I know how to do gradient descend etc., but here I need to minimize the function L by iterating over K and I don't really know how to approach it. I'd expect something of this sort: $K:=K-f(\nabla(L))$, but I don't know what.</p> <p>*note: It might have something to do with the Euler-Largange method ($L_x-L_t\left(L_{x'}\right)=0$) but I'd have to do it iteratively if any...</p> <p>Appreciate any help.</p> http://mathoverflow.net/questions/103935/brownian-bridge-in-two-variables Comment by id0 id0 2012-08-05T10:57:41Z 2012-08-05T10:57:41Z I wrote it to differentiate it from a 2D BM which has BM in x and y axis which gives us a &quot;line&quot;. http://mathoverflow.net/questions/85325/optimization-of-a-matrix-with-an-objective-function-for-ml Comment by id0 id0 2012-01-11T07:11:42Z 2012-01-11T07:11:42Z This is not a HW question, I didn't specify any other terms because I'm not sure about what I want to do yet. Obviously K=0 is a solution but since I do it iteratively I may not get there. The general form of L would be rather the sum of both L's I specified, so the exponents have a meaning. Also, I didn't decide yet whether I want the Frobenius or L2 norm. My question is more technical - Say I have a matrix K of size 3x3, how do I iteratively modify it so that I minimize L. Thanks.