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|---|---|---|
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| age | 28 | |
| visits | member for | 2 years, 9 months |
| seen | 4 hours ago | |
| stats | profile views | 3,198 |
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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13h |
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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 |
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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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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 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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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 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 18 |
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Proof that maximizing a function is equivalent to minimizing its negative If you can complete the proof, then there's no tricks. If you can't complete the proof, then you need to worry about tricks. |
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Mar 18 |
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Proof that maximizing a function is equivalent to minimizing its negative $f$ is maximized at $x$ if $f(x)\ge f(y)$ for all $y$. $-f$ is minimized at $x$ if $-f(x)\le -f(y)$ for all $y$. Can you complete the proof? |
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Mar 15 |
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Is any natural number e.g. 0 a count? Count the number of tyrannosaurids in Buckingham Palace. |
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Mar 15 |
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Operators and Functions This is the account that posted the question. This is your current account. They are different. Try following these instructions. |
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Mar 15 |
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Why does $ (A^T x) · y = x · (A y) $ hold? Assuming the inner product is $u\cdot v=u^Tv$, just expand out $(A^Tx)^Ty$ and $x^T(Ay)$ and compare. |
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Mar 14 |
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What are $(-1)^\infty$ and $1^{-\infty}$? @Dennis: Evidence suggests otherwise. |
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Mar 13 |
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Array resize problem You got a different fit but the graph didn't change at all? |
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Mar 13 |
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A Question About Linear Interpolation Looks a little prettier as $(k_2A-k_1B)/(k_2-k_1)$. |
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Mar 13 |
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The multiplication of 2D vectors produces what? You should get out of the habit of calling this multiplication of 2D vectors, though, precisely because it does not behave like a natural operation on vectors. What you're doing is interpreting vectors as complex numbers, doing multiplication of complex numbers, and then reinterpreting the result as a vector. As an analogy, there's no such thing as addition of bit strings; you can only interpret bit strings as numbers and then add the numbers, but that depends on the choice of how you interpret the bits as unsigned, two's complement, or floating-point, etc. |
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Mar 13 |
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The multiplication of 2D vectors produces what? I think I understand where you're coming from. With vectors in general, the $x$-axis is not special, in that you can always change your basis and make some other directions your axes. So defining things in terms of the $x$-axis seems arbitrary and suspicious. But multiplication does make the $x$-axis special: the unit vector in the positive $x$-axis is the only vector which when multiplied with any other vector gives the other vector back. This also means that you're no longer allowed to change your basis: if the transformation is denoted $T(u)$, then $T(u)T(v)\ne T(uv)$. |
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Mar 12 |
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Array resize problem If this is an exercise problem, it would help if you share what your thoughts are on how to approach it and what you have already tried. |
