376 reputation
18
bio website
location Universidade de São Paulo, Brazil
age 29
visits member for 2 years
seen Mar 21 '13 at 20:24

I am currently a post-doc at the Physics department at the University of Sao Paulo. My interests are in Statistical Physics, stochastic processes and magnetism. More importantly, I really value simple and solid explanations to important problems in any science.


Jan
14
comment Average distance between random points inside a cube
Oh! Yeah, I think that is it. The nearest-neighbour distance. I got everything confused.
Jan
14
comment Average distance between random points inside a cube
I am still confused about where the concentration of points enter. I mean, if $n$ is large, than the average distance between them should be smaller, but I don't see how that enters the calculation. Anyway, thank you for the help.
Nov
29
comment Solving for the trace of a matrix
This is incredible. Thank you so very very much.
Nov
27
comment Solving for the trace of a matrix
I have come across that manipulation but, unfortunately, it does not remove $\Theta$ so it doesn't really work much. But, in any case, thanks for your help.
Nov
27
comment Solving for the trace of a matrix
@Berci the matrix $\Theta$ is uniquely determined from the Lyapunov equation. Hence so is $F$.
Nov
17
comment Reference suggestion: eigenvalues of tridiagonal matrices
@Elias Great. Thank you very much.
Sep
10
comment Discrete Analogue of the Fundamental Theorem of Calculus
Good Point. :) Once again, thank you.
Sep
10
comment Discrete Analogue of the Fundamental Theorem of Calculus
I see. But isn't this notation misleading? I mean, in continuous calculus you write $d/dx$ to specify the derivative is with respect to $x$. Wouldn't $\Delta_n$ be a more adequate notation? And is this common in difference calculus literature? Anyway, thank you very much for the answer.
Aug
31
comment Modification of the continuous time Lyapunov Equation
The idea in your answer is probably unfeasible, since my system has $n > 200$. Could you point out a reference for this pole-place method? By the way, thanks for the support.
Aug
21
comment Calculate a whitening matrix without using inverses?
Isn't computing the entire eigenvector matrix also expensive, even for a symmetric matrix? I wonder if Cholesky itself isn't faster.
Aug
14
comment Solving for specific entries in a Lyapunov Equation
Actually, I have been looking at the web and haven't yet found a method for solving the eq. for B. Any ideas on where to look?
Aug
14
comment Solving for specific entries in a Lyapunov Equation
Wow, this is great. Thank you! I'll start testing this idea right away and post some results as soon as they come out.
Aug
9
comment Solving for specific entries in a Lyapunov Equation
@dato, Sorry I don't understand.
Aug
9
comment Solving for specific entries in a Lyapunov Equation
The solution of the Lyapunov equation, $R$, will be symmetric and positive definite (it is actually a covariance matrix). What I can prove is that $C$ is anti-symmetric ($C^\text{T} = -C$)
Jul
28
comment Partial Fractions Expansion of $\tanh(z)/z$
Yeah. Probably. Hehe. It's just that I never know how to deal with sums in any other way than comparing it to other sums. Again, thank you for the answer J.M.
Jul
28
comment Partial Fractions Expansion of $\tanh(z)/z$
@jm this is great; does all such formulas rely on manipulating other known products and sums? Isn't there, for instance, a Fourier transform or generating function approach (or something...)? Again, thank you for the support.
Jul
27
comment Approximate solution for the root of a non-linear function
Let $F_\pm(t) = e^t (g \cos(\omega t-\phi) \pm b)$. The first point, $t_0$ say, is computed from either $F_\pm(t_0) = F(0) \mp \alpha$, where $\alpha$ is a positive constant. From there one the roots are computed sequentially as above.
Jul
27
comment Approximate solution for the root of a non-linear function
Thank you all very much for the support and thank you @LeonidKovalev for the bounty.
Jul
26
comment Approximate solution for the root of a non-linear function
Yes Mr. Badwaik. I want the first $t_1$ after $t_0$.
Jul
25
comment Distance between discrete random variables
Mr. Schmuland, thank you for your answer Indeed, I was interpreting $Y$ as signifying the G's in your answer, thinking they could all be treated as a single variable. Is that impossible? This confuses me: suppose I take the limit of both $n$ and $k$ going to $\infty$, but such that k/n remains fixed. Then $Y$ represents E(G's)? Thank you again for your time.