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I hereby authorize whoever it may concern to post my comments as answers if they wish, whether as community wiki or otherwise if you like imaginary internet points.


17h
comment Is there any theorem about figures of equal area and perimeter being congruent?
@Semiclassical: I'll save you the effort. Let the shape be given in polar coordinates by $r(\theta) = 1 + f(\theta-\alpha) + g(\theta-\beta)$ where $f$ and $g$ are bump functions, i.e. smooth and compactly supported. Now vary $\alpha$ and $\beta$ while the supports do not overlap.
17h
comment Is there any theorem about figures of equal area and perimeter being congruent?
@Semiclassical: Consider a circle with two independent "bumps"...
2d
comment Granted I have NE and SW coordinates for a rectangle, how do I get the center point?
...and how do you define center point? Unless you already have a precise definition you need to use, I would argue that averaging the coordinates is perfectly fine.
2d
comment The $R^x$ notation?
And of course, just like the usual rules of exponentiation, $\mathbb R^1$ is $\mathbb R$ itself, the real line. Fun exercise: What is $\mathbb R^0$?
2d
comment Drawing a triangle from medians
How to construct a triangle given its three medians‌​.
2d
comment If the Planck length exists, why doesn't it follow then that the world is one-dimensional?
Even if space weren't quantized, you could represent any point by one parameter.
Jul
18
comment What's the difference between a cyclic and periodic function?
Your link gives me "To view the definition of cyclic function, activate your Merriam-Webster Unabridged Dictionary FREE TRIAL now!" Can you just quote the example in your question? Although I'm guessing Greg's answer is probably what you need.
Jul
18
comment What's the difference between a cyclic and periodic function?
Can you give an example of where you saw a function described as "cyclic"?
Jul
17
comment Using l1 magic toolbox for compressive sensing : Positive definite matricies.
If the columns of $\Phi$ represent the projected binary patterns, then shouldn't you have $b=\Phi^Tx$ and not $b=\Phi x$? ...Also you probably want to minimize the $L^1$ norm of $\alpha$, not $x$. I don't think positive definiteness should have anything to do with it because the matrices aren't square in the first place so can't possibly be positive definite.
Jul
16
comment Are “constrained linear least squares” and “quadratic programming” the same thing?
I found a few typos in your derivation, so I fixed them. Please check that my edit is correct.
Jul
16
comment Are “constrained linear least squares” and “quadratic programming” the same thing?
Every constrained linear least-squares problem can be expressed as an instance of quadratic programming, as Joel's answer sort of shows ($Q\gets Q^TQ$, $c\gets Q^Tc$). But not every quadratic programming problem can be expressed as a constrained linear least-squares problem, because $Q$ may not be positive definite.
Jul
16
comment Restore the signum of abs(sinc(x))
Well, the smallest value ${\rm sinc}(x)$ ever attains is about $-0.217$, so if $|{\rm sinc}(x)|\ge0.218$ then you know ${\rm sinc}(x)$ must be positive. But otherwise, no.
Jul
15
comment Box-Muller method for correlated normals
I still don't see why you couldn't do exactly the same thing with uncorrelated variables and then multiply by a matrix, but I won't pester you about it.
Jul
15
comment Why Maximize Expected Value?
The distribution which minimizes the variance is of course the one-coin-per-box distribution, with zero expected return and zero variance. :)
Jul
15
comment What is the edge called that converts a tree to a directed acyclic graph?
These correspond to what would be cycles if you interpreted your DAG as an undirected graph. So possibly something related to the phrase undirected cycle?
Jul
14
comment Variational Principles: Lagrange Multipliers
Tip: Use \| instead of ||, it looks better: $\|\mathbf x\|$ vs. $||\mathbf x||$.
Jul
14
comment Box-Muller method for correlated normals
Is there a reason you are seeking an alternative approach?
Jul
14
comment Apparent Paradox in the Idea of Random Numbers
Related: Probability of picking a random natural number
Jul
14
comment Expressing the probability density function of $Ax$ in terms of the pdf of $x$
Well... the question used to be specifically about scale-invariant probability distributions, not about scaling arbitrary probability distributions in general. See, for example, the link at the end of the post. I'm not convinced that the edited title matches the OP's intent.
Jul
13
comment Metric for movement in 2D space
The average velocity of a particle over some time interval is just (position at end of interval - position at start of interval)/(duration of interval).