8,845 reputation
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location France
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visits member for 2 years, 5 months
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I'm a postdoc at LIUM in France, working in Machine Learning (statistical machine translation), although my thesis was on mathematical analysis of Evolutionary Algorithms (EAs), therefore my skills revolve around probability, Markov chains, calc/analysis, asymptotics and a bit of combinatorics.

I'm here mostly to learn and improve my skills, so please don't expect much rigor or proficiency from me.

This is my Academia profile if you are interested in my work for some reason.


Jan
12
comment When $\frac{C(n, k)}{n^{k-1}} > 1$?
$\frac{735}{6!} \approx 1.02$
Jan
12
answered When $\frac{C(n, k)}{n^{k-1}} > 1$?
Jan
11
answered Handshake counting problem
Jan
11
answered in a mountain climbing expeditions 5 men and 7 women are to walk
Jan
10
answered Evaluate $\lim_{x \to 4}\frac{(2x)^{1/3} - 2}{\sqrt{x} - 2}$ without L'Hospital rule
Jan
7
comment Find $\lim_{x \to 0}\frac{x-\sin(x)\cos(x)}{\sin(x)-\sin(x)\cos(x)}$
you are welcome
Jan
7
comment Find $\lim_{x \to 0}\frac{x-\sin(x)\cos(x)}{\sin(x)-\sin(x)\cos(x)}$
I agree. All I meant that $\frac{O(x^3)}{6}$ is a strange notation. Usually we either have $\frac{x^3}{3!}$ or $O(x^3)$ since $O(\cdot)$ implies an asymptotic constant
Jan
7
comment Find $\lim_{x \to 0}\frac{x-\sin(x)\cos(x)}{\sin(x)-\sin(x)\cos(x)}$
what you probably meant was $\sin x = x -\frac{x^3}{3!} + O(x^5)$
Jan
7
comment Proof that $e^x$ can be expressed in a series of ascending powers of $x$
@imulsion: what you have in the post is a partial expression for this function. It's like saying that $a^2$ is the area of the triangle instead of $\frac{a^2}{2}$
Jan
7
comment Proof that $e^x$ can be expressed in a series of ascending powers of $x$
the definition of $e^x$ is certainly wrong
Jan
6
comment How can I prove that $\int_{0}^{\infty }\frac{\log(1+x)}{x(1+x)}dx=\sum_{n=1}^{\infty }\frac{1}{n^2}$
Thanks. I understand that $\lim_{u} \frac{u}{e^u -1} = 1$, still a bit unclear why it justifies $\frac{1}{e^u -1} = \sum_k e^{-uk}$ expansion.
Jan
6
comment How can I prove that $\int_{0}^{\infty }\frac{\log(1+x)}{x(1+x)}dx=\sum_{n=1}^{\infty }\frac{1}{n^2}$
one thing: to use the Binomial expansion we need $|x|<1$, the inequality is strict, while $e^u =1$ when $x=0$. Why is this not an issue?
Jan
5
answered If event A is independent with event B, then is the subset of A is independent with B?
Jan
2
comment Probability for a word to start with $\text{2,0,0,4}$
all letters are unique
Jan
2
answered Probability for a word to start with $\text{2,0,0,4}$
Jan
2
comment Using generating function determine $u_n$
Note $1+8z -9 z^2 = (1-z)(1+9z) = \phi_1$, so on the RHS you'll have $\frac{24}{(1-3z) \phi_1}$- split it in three, the other ones $\frac{a_0}{\phi_1} +\frac{a_1 z}{\phi_1} + \frac{8 a_0 z}{\phi_1}$, which are elementary
Jan
2
comment Using generating function determine $u_n$
What exactly is you complication? What do you get?
Jan
2
revised Using generating function determine $u_n$
added 1 character in body
Jan
2
comment Using generating function determine $u_n$
you have a typo in the second term on the LHS: it should be $\sum_{k=1}^{\infty} u_{k+1}x^k$
Jan
2
answered Using generating function determine $u_n$