User leonbloy - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T00:59:16Z http://mathoverflow.net/feeds/user/5428 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/82447/2d-moment-of-chebyshev/82461#82461 Answer by leonbloy for 2d moment of chebyshev leonbloy 2011-12-02T14:19:29Z 2011-12-02T14:19:29Z <p>If you are interested in approximation for large $n,d$, with a simple Poissonization argument I get:</p> <p>$$E(X^{2d}) \approx n^{2d} \left( \frac{1+e^{-2\lambda}}{2} \right)^n$$ </p> <p>where $\lambda = \frac{2d}{n}$</p> http://mathoverflow.net/questions/8846/proofs-without-words/69022#69022 Answer by leonbloy for Proofs without words leonbloy 2011-06-28T14:42:08Z 2011-06-28T14:42:08Z <p>(I'd post this as a comment to Mariano Suárez-Alvarez, but I've not enough rep). From a <a href="http://math.stackexchange.com/questions/44759/combinatorial-proof-that-binomial-coefficients-are-given-by-alternating-sums-of-s/44782#44782" rel="nofollow">ME thread</a>.</p> <p>$$\sum_{k=1}^n (-1)^{n-k} k^2 = {n+1 \choose 2} = \sum_{k=1}^n \; k = \frac{(n+1) \; n}{2}$$</p> <p><img src="http://i.stack.imgur.com/2s7sk.png" alt="alt text"></p> http://mathoverflow.net/questions/63789/probability-of-a-random-walk-crossing-a-straight-line/64444#64444 Answer by leonbloy for Probability of a Random Walk crossing a straight line leonbloy 2011-05-10T01:42:27Z 2011-05-10T14:54:59Z <p>(Just a hint. Should be a comment more than an answer, but don't have enough rep)</p> <p>It seems interesting the slightly more general problem in which the initial distance to the line is greater than zero - or that the line has the equation $a n + b$ Considering $a$ fixed and $b$ variable, one can get (if I'm not mistaken) a the following equation on $P(b)$ (probability that the process crosses the line) as:</p> <p>$P(b)= \left\{ \begin{array}{ll} \frac{1}{2}\left[ P(b+a-1)+P(b+a+1) \right] &amp; \mbox{if } b \geq 0 \\ 1 &amp; \mbox{if } b &lt; 0 \end{array} \right.$</p> <p>We want a solution (apart from the trivial $P(b)=1$) that goes to zero as $b \to \infty$ , and we are specially interested in $P(0^+)$ Does not seem easy, seems very sensitive to the parameter $a$. I believe that if $a$ is rational, $a=m/n$, the funcion has discontinuites at points $k/n$. </p> http://mathoverflow.net/questions/23478/examples-of-common-false-beliefs-in-mathematics/64424#64424 Answer by leonbloy for Examples of common false beliefs in mathematics. leonbloy 2011-05-09T20:05:37Z 2011-05-09T20:05:37Z <blockquote> <p>"Suppose that two features $[x,y]$ from a population $P$ are <strong>positively correlated</strong>, and we divide $P$ into two subclasses $P_1$, $P_2$. Then, it cannot happen that the respective features ( $[x_1,y1]$ and $[x_2,y_2]$) are <strong>negatively correlated</strong> in both subclasses</p> </blockquote> <p>Or more succintly:</p> <blockquote> <p>"Mixing preserves the correlation sign."</p> </blockquote> <p>This seems very plausible - almost obvious. But it's false - see <a href="http://en.wikipedia.org/wiki/Simpson%27s_paradox" rel="nofollow">Simpon's paradox</a></p> http://mathoverflow.net/questions/25374/duplicate-detection-problem/25419#25419 Answer by leonbloy for duplicate detection problem leonbloy 2010-05-20T20:54:27Z 2010-05-20T20:54:27Z <p>Basically David's approach: we fix $M$ = number of bits storage, and compute the indicator $h = XOR ( hash_M (a [i] ) )$</p> <p>where $hash_M$ is a hash function to $M$ bits (eg MD5 masked to M bits). We decide that it is a permutation without repetitions by comparing with the same indicator for the ordered array (1..N). This is order N. And there is a probability of error which should be around $1/2^M$... if I'm not mistaken.</p> http://mathoverflow.net/questions/67648/fitting-an-ellipse-to-an-arbitrary-polygon Comment by leonbloy leonbloy 2012-12-19T15:59:00Z 2012-12-19T15:59:00Z Another heuristic to adapt the &quot;fit polygon&quot; problem to the &quot;fit points&quot; recipe would be to insert equispaced phantom points along the poygon sides.