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Systems biologist.


Nov
8
comment Calculating the probability that a cord makes a knot
Thanks so much, that's what I'm looking for. If you post your comment as an answer I'll accept it.
Nov
7
comment Is there a good online dictionary/encyclopedia for mathematics?
If you read Japanese, the most recent (Japanese 4th) edition of the Encyclopedic Dictionary of Mathematics has an accompanying CD-ROM that contains PDF files of the 4th and 3rd (equivalent to English 2nd) edition, which I find extremely convenient. (But of course they are not for free.)
Nov
7
comment Proving a large factorial expression for $1 \le m \le n - 1$
math.stackexchange.com/questions/70190/…
Nov
7
comment Higher order derivative of parameter curves
$\frac{d^2y}{dx^2}=\frac{d}{dx}\left(\frac{dy}{dx}\right)$, and $\frac{d}{dx}(\cdots)=\frac{dt}{dx}\frac{d}{dt}(\cdots)$
Nov
5
comment How to add cosines with different phases using phasors
$\sqrt{14+8\sqrt{2}}$, not $\sqrt{14+\sqrt2}$
Nov
4
comment From given equality find that $p$ for which equality have at least one positive root
(2) has a typo: $\frac{1}{2p}\sqrt{\cdots}$, not $\frac12\sqrt{\cdots}$
Oct
15
comment Population Dynamics model
"Mathematical demography" may be a useful keyword.
Oct
14
comment Filling out an $n \times n$ square grid with $0$s and $1$s
Have you tried solving the case when $n$ is small, e.g. $n=1,2,3,4,5,\ldots$?
Oct
7
comment For which n are there primitive Pythagorean triples with legs of lengths a and a+n?
The title says "primitive", so $GCD(a,n,c)=1$ is assumed?
Oct
6
comment How to visualize the Gaussian curvature of a 3D surface?
graphics.ucsd.edu/~iman/Curvature
Oct
1
comment fractional linear transformations
@Zarrax I see. +1 for your nice argument.
Sep
30
comment fractional linear transformations
Nice argument, but I think it is not immediately clear whether the transformation takes the unit circle to "the whole of" the unit circle.
Sep
30
comment fractional linear transformations
$w=f(z)=(3z+i)/(-iz+3)$ is obviously not equal to $z$. The above is a common procedure for finding the image of a function. Do you understand that $|z|<1$ is equivalent to $|3w-i|<|iw+3|$? Which means, if $|z|<1$, its image $w=f(z)$ must satisfy $|3w-i|<|iw+3|$; and if $w$ satisfies $|3w-i|<|iw+3|$, it must be the image of some $z$ satisfying $|z|<1$. This shows that $\{w\in \mathbb{C}\mid|3w-i|<|iw+3|\}$ is the desired image.
Sep
27
comment Multivariate Taylor Series Derivation (2D)
This is not a rigorous proof: Suppose that one can write $f(x,y)=f(a,b)+A(x-a)+B(y-b)+C(x-a)^2+D(x-a)(y-b)+E(y-b)^2+\cdots$, how can the values $A, B, C, D, E, \dots$ be determined?
Sep
27
comment How to approach mathematical modeling of the human heart problem?
@ChesnokovYuriy Have you already checked "Mathematical Physiology" by Keener & Sneyd? It includes chapters on the human heart (Chapter 12) and can be a good starting point.
Sep
14
comment twice differentiable function (question from exam)
Nice answer (the above equation can be obtained using integration by parts twice). I'm also interested in its origin. My hunch was that the coefficient $1/12$ could be related to the trapezoidal rule, but I wasn't able to complete the proof along that line.
Sep
7
comment How do you find the optimal value for this function?
Thanks for the fix.
Sep
4
comment Hilbert transform of white noise
Thanks so much! This gives me the motivation to learn more about the theory of probability.
Sep
2
comment Hilbert transform of white noise
Thank you Sasha for your comment.
Sep
1
comment Hilbert transform of white noise
Let me explain the background. For a real-valued signal $f(t)$ (oscillatory but noisy), by applying the Hilbert transform $H$ one can determine its phase $\phi(t)$: $f(t) + H[f(t)]i =A(t)e^{i\phi(t)}$. I would like to know how noise in the original data $f(t)$ can affect the precision of determination of $\phi(t)$.