linello
Reputation
Top tag
Next privilege 250 Rep.
 Sep 27 awarded Curious Sep 26 asked Is $d(i,j) = 1-\textrm{corr}(i,j)$ a metric? Sep 24 awarded Autobiographer Jul 23 comment Multiple Hypergeometric Distributions If the draws are independent then you can multiply the probabilities. Jul 10 comment Is There a Continuous Analogue of the Hypergeometric Distribution? Thanks for the good reference. What I'm still missing is how is possible to compute the cumulative hypergeometric distribution given the Wiener-Askey chaos expansion. Why isn't the sum approximable with an integral as follows? $\sum_{i=m_i}^m \binom{p_i}{i}\binom{p-p_i}{m-i}/\binom{p}{m} \approx \int_{m_i-1/2}^{m+1/2} \binom{p_i}{x}\binom{p-p_i}{m-x}/\binom{p}{m} dx$ where the binomial coefficients are evaluated with the help of $\Gamma$ function as $\binom{a}{b} = \frac{\Gamma(a+1)}{\Gamma(b+1)\Gamma(a-b+1)}$ Jul 10 comment Is There a Continuous Analogue of the Hypergeometric Distribution? can you please point me to some good explanation of the continuous Hahn polynomials? I'm interested in understanding if it is possible to compute the hahn polynomial from the following $_3F_2({1,mi-m,mi-pi},{mi+1,mi+p-pi-m+1},1)$ which comes a simplification of the hypergeometric cumulative distribution $\sum_{i=mi}^m \binom{pi}{i} \binom{p-pi}{m-i}/\binom{p}{m}$ Jul 9 comment Is There a Continuous Analogue of the Hypergeometric Distribution? Is it also possible to use the Gauss-Hermite polynomial chaos for the cumulative hypergeometric distribution? Jun 17 awarded Peer Pressure Apr 29 awarded Tumbleweed Jun 19 accepted Texture mapping and conformal transformation Jun 19 comment Texture mapping and conformal transformation Oh yes! I've been wrong putting $(r,\theta)$ instead of $(r \cos(\theta), r \sin(\theta) )$ this in fact makes much more sense! Stupid me, seeing the same thing for 2 days hides the evident things! This is the result of conformal requirements: and the resulting shader code float rho = sqrt(v.x*v.x+v.y*v.y); float theta = atan(v.y,v.x); float a=1.0; float r = (pow(4*rho*rho+1,1.5) -1)/(12*a) ; texture_coordinate = vec2(r*cos(theta),r*sin(theta)); gl_Position = gl_ModelViewProjectionMatrix*v the effect is the following: imgur.com/jqusOyl Jun 19 comment Texture mapping and conformal transformation Hey, thanks for the ideas! This is the result of conformal and constant area requirements. imgur.com/ygrMoFw My biggest problem is that, i think, the theta is wrong. This is basically the GLSL code to do this texture mapping if your are interested (the constant area case) float rho = sqrt(v.x*v.x+v.y*v.y); float theta = (atan(v.y,v.x)+pi/2)/(pi); float s= sqrt(4*rho*rho+1); float a=1.0; float r = (pow(4*rho*rho+1,1.5) -1)/(12*a) ; texture_coordinate = vec2(r,theta); gl_Position = gl_ModelViewProjectionMatrix*v; Jun 18 comment Texture mapping and conformal transformation Thanks for the accurate response. In fact I would also like to understand how to get the constant area element. Excuse me for the double question. You are suggesting that my new coordinates should be $\theta = \arctan(y/x)$ and the $r(\rho)$ in your last equation? Jun 17 asked Texture mapping and conformal transformation Jun 14 awarded Supporter Jun 14 awarded Commentator Jun 14 comment Is nonlinear conjugate gradient a quasi-newton optimization technique? Thank you, this question is what I was looking for. Jun 7 asked Is nonlinear conjugate gradient a quasi-newton optimization technique? Sep 27 comment Extracting angular velocity tensor from orthogonal matrices Yes, this is not correct. I meant I would like to compute $\mathbf{Y}$ in a more robust manner, but I think that given its definition, it's obvious it approximate the identity when $\Delta t \rightarrow 0$, so for high sampling rate, no chances... It seems to me so strange that there are no methods to extract angular velocity from discrete time systems... Sep 26 comment Extracting angular velocity tensor from orthogonal matrices Thanks, I understand, when the sampling rate increases $\mathbf{Y}$ approaches the identity, but maybe can be useful to derive a better discrete approximation to Y. Is this the case? How to deal (if possible) with better derivative approximation scheme supposing that I'm able to have $R(t),R(t-1),R(t-2),...,R(t-k)$?