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| bio | website | |
|---|---|---|
| location | ||
| age | 28 | |
| visits | member for | 2 years, 9 months |
| seen | 2 mins ago | |
| stats | profile views | 3,202 |
Almost all of the questions on the front page these days are homework questions or textbook exercises. I think I'll be spending a lot less time here.
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4h |
comment |
Quaternion exponential map, rotations and interpolation I meant that if $\mathfrak q$ is storing the logarithm of the actual quaternion $\exp\mathfrak q$ representing the orientation, and you wanted to post-compose another rotation represented by a quaternion $p$, the new orientation would be $\exp(\mathfrak q)\cdot p$, and you would store its logarithm $\log(\exp(\mathfrak q)\cdot p)$ in $\mathfrak q$. If someone overloaded the addition operator on the quaternion type to do multiplication instead, this would explain it. |
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12h |
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Quaternion exponential map, rotations and interpolation Are you sure it's not actually doing $\ln(\exp(\mathfrak q)\cdot\mathfrak p)$ instead? That would make a lot more sense, and you never know if someone coded the right thing under the wrong function names... |
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1d |
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Discretizing a cosine function? This is known as aliasing. |
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1d |
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What is the Greek version of $\;\cal{quod~erat~demonstrandum}\;$? If your question is "How do I enter ὅπερ ἔδει δεῖξαι in a TeX file?", you should ask it on tex.stackexchange.com instead. |
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2d |
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Determine direction of minimum overlap of convex polygons For infinitesimally small $\vec r$, the optimal direction is perpendicular to the line joining the two points where the boundaries of $P$ and $Q$ intersect. |
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May 16 |
comment |
Solve for an Ellipse Tangent to 2 Lines I think this is a duplicate of this previous question. There are infinitely many ellipses through two points with prescribed tangents, as described in my answer. |
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May 16 |
revised |
Solve for an Ellipse Tangent to 2 Lines added 19 characters in body; edited tags |
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May 8 |
awarded | Nice Question |
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Apr 30 |
awarded | Necromancer |
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Apr 22 |
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Can one sample uniformly from the surface of an $n$-sphere of non-unit radius using normal r.v.'s? Yes. ${}{}{}{}$ |
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Apr 18 |
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Is this the right equation for this 3D surface? Its proper name is $\operatorname{sinc}(r)$ where $r=\sqrt{x^2+y^2+z^2}$. |
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Apr 14 |
awarded | Necromancer |
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Apr 8 |
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(Computationally) Simple sigmoid You can try just using $f(x)=\dfrac{g(1-x)}{g(x)+g(1-x)}$ where $g(x)=\exp(-1/x)$, whose derivatives of all orders are zero at the endpoints. |
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Apr 1 |
awarded | Nice Answer |
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Mar 27 |
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how to transform a space to optimally separate data How about the fixed transformation to a $n(n+1)/2$-dimensional space of quadratic terms, $(x_1,x_2,\ldots,x_n) \mapsto (x_1^2,2x_1x_2,\ldots,2x_1x_n,\ x_2^2,\ldots,2x_2x_n,\ \ldots,\ x_n^2)$? Now $d(x)^2=\sum m_{ii} x_i^2+2\sum m_{ij}x_ix_j$ is linear in this space, so you can do linear SVM here and your users don't have to contrive any kernels themselves. The only thing is that this maximizes $\min\limits_{x\in B} d^2(x)-\max\limits_{x\in A} d^2(x)$ subject to $\lVert M\rVert_F=1$ instead of your proposed criterion. |
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Mar 27 |
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how to transform a space to optimally separate data A more common approach to classification problems (see linear support vector machine) is to find an optimal separating hyperplane rather than an ellipsoid; that is, find the unit vector $u$ which maximizes $\min\limits_{x\in B} u^Tx - \max\limits_{x\in A}u^Tx$. Is there any reason why you wouldn't want to try this? |
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Mar 26 |
revised |
manifold projection deleted 176 characters in body |
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Mar 23 |
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What's the difference between direction, sense, and orientation? Going by "Orientation and sense together determine the direction of a vector", I guess what the author of the linked PDF means is that $v$ and $-v$ have the same orientation but opposite sense. I don't think this is standard usage. |
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Mar 20 |
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In need of tips/suggestions when to add or multiply probabilities "the probability is the ratio of the number of possible pairs with one black and one white ball to the total number of possible pairs. This equals $(4\times3)/\binom72=4/7$" |
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Mar 19 |
reviewed | Reject suggested edit on Tensor and Kronecker product |
