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Closed form for $\int_0^\infty\frac{1}{(1+x^2)^s}\,dx$ when $s\in (0.5,\infty)\setminus\mathbb{N}$ Where is the Layers panel in Blender 2.8? How to add border to listview and different row colors at the same time GP 1.2.10(b) The tangent space $T_{(x,x)}(\triangle)$ is the diagonal of $T_x(X) \times T_x(X).$ If $\triangle$ is the diagonal of $X \times X$, show that its tangent space $T_{(x,x)}(\triangle)$ is the diagonal of $T_x(X) \times T_x(X).$   I don't have the slightest idea on how to do this.  By definition, the tangent space of $X$ at $x$ is the image of the map $d\phi_0: \mathbb{R}^k \rightarrow \mathbb{R}^N$, where $x + d\phi_0(v)$ is the best linear approximation to $\phi: V \rightarrow X$ at 0. $\phi: V \rightarrow X$ is a local parametrization around $x$, $X$ sits in $\mathbb{R}^N$ and $V$ is an open set in $\mathbb{R}^k$, and $\phi(0) = x$.  Thanks. Installing ChatJax bookmark on the iPad and iPhone How do I get a file extension in PHP? Strip HTML from Text JavaScript How can one refute John Searle's "syntax is not semantics" argument against strong AI? In my bash script I have an external (received from user) string, which I should use in sed pattern.  REPLACE="&lt;funny characters here&gt;" sed "s/KEYWORD/$REPLACE/g"   How can I escape the $REPLACE string so it would be safely accepted by sed as a literal replacement?  NOTE: The KEYWORD is a dumb substring with no matches etc. It is not supplied by user. Is it possible to plot a graph of any shape? In school, I have learnt to plot simple graphs such as $y=x^2$ followed by $y=x^3$.  A grade or two later, I learnt to plot other interesting graphs such as $y=1/x$, $y=\ln x$, $y=e^x$. I have also recently learnt about trigonometric graphs and circle equations. In the internet, I have seen users posting graphs of different shapes like a heart-shaped graph and a Batman logo-shaped graph. I am sure there are numerous more graphs that I have yet to see. Seeing that the graphs can be shaped into shapes like the Batman logo and a heart brings me to my question: Is it possible to plot a graph of any shape regardless of its complexity? Perhaps, shaped into an outline of a person or a landmark? Why or why not? Notation for functions vs. numbers Knife tool doesn't cut obscured edges I'm using Blender 2.66,  I find that the knife tool (K) doesn't work the way it used to.     Dragging across an obscured edge, even if selected, doesn't cut it. There seems to be no way to activate the option to do a midpoint cut or multiple cuts. Modular arithmetic: division, fractions, solving linear congruences What is the difference between logistic regression and Fractional response regression? As far as I know, the difference between logistic model and fractional response model (frm) is that the dependent variable (Y) in which frm is [0,1], but logistic is {0, 1}. Further, frm uses the quasi-likelihood estimator to determine its parameters. Normally, we can use glm to obtain the logistic models by glm(y ~ x1+x2, data = dat, family = binomial(logit)). For frm, we change family = binomial(logit) to family = quasibinomial(logit). I noticed we can also use family = binomial(logit) to obtain frm's parameter since it gives the same estimated values. See the following example library(foreign) mydata &lt;- read.dta(&quot;k401.dta&quot;)   glm.bin &lt;- glm(prate ~ mrate + age + sole + totemp,                 data = mydata, family = binomial('logit')) summary(glm.bin)  return,  Call: glm(formula = prate ~ mrate + age + sole + totemp,      family = binomial(&quot;logit&quot;),      data = mydata)  Deviance Residuals:      Min       1Q   Median       3Q      Max   -3.1214  -0.1979   0.2059   0.4486   0.9146    Coefficients:               Estimate Std. Error z value Pr(&gt;|z|)     (Intercept)  1.074e+00  8.869e-02  12.110  &lt; 2e-16 *** mrate        5.734e-01  9.011e-02   6.364 1.97e-10 *** age          3.089e-02  5.832e-03   5.297 1.17e-07 *** sole         3.636e-01  9.491e-02   3.831 0.000128 *** totemp      -5.780e-06  2.207e-06  -2.619 0.008814 **  --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  (Dispersion parameter for binomial family taken to be 1)      Null deviance: 1166.6  on 4733  degrees of freedom Residual deviance: 1023.7  on 4729  degrees of freedom AIC: 1997.6  Number of Fisher Scoring iterations: 6  And for family = quasibinomial('logit'), glm.quasi &lt;- glm(prate ~ mrate + age + sole + totemp,   data = mydata ,family = quasibinomial('logit')) summary(glm.quasi)  return,  Call: glm(formula = prate ~ mrate + age + sole + totemp,      family = quasibinomial(&quot;logit&quot;),      data = mydata)  Deviance Residuals:      Min       1Q   Median       3Q      Max   -3.1214  -0.1979   0.2059   0.4486   0.9146    Coefficients:               Estimate Std. Error t value Pr(&gt;|t|)     (Intercept)  1.074e+00  4.788e-02  22.435  &lt; 2e-16 *** mrate        5.734e-01  4.864e-02  11.789  &lt; 2e-16 *** age          3.089e-02  3.148e-03   9.814  &lt; 2e-16 *** sole         3.636e-01  5.123e-02   7.097 1.46e-12 *** totemp      -5.780e-06  1.191e-06  -4.852 1.26e-06 *** --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  (Dispersion parameter for quasibinomial family taken to be 0.2913876)      Null deviance: 1166.6  on 4733  degrees of freedom Residual deviance: 1023.7  on 4729  degrees of freedom AIC: NA  Number of Fisher Scoring iterations: 6  The estimated Beta from both `family` are the same, but the difference is the SE values.  However, to obtain the correct SE, we have to use `library(sandwich)` as in this [post][1].  Now, my questions:  1. What is the difference between these two codes? 2. Is frm about to obtain robust SE?  If my understanding is not correct, please give some suggestions.      [1]: https://stackoverflow.com/questions/37584715/fractional-response-regression-in-r Is there a contraction for "I was"?    There are contractions for "I am" (I'm), "I will" (I'll), "I have" (I've), "I would" (I'd), and yet the simple past tense seems conspicuously missing. Why is that? Does that reasoning apply to "I did" and "I had" as well? Let's say I am building a logistic regression model where the dependent variable is binary and can take the values $0$ or $1$. Let the independent variables be $x_1, x_2, ..., x_m$ - there are $m$ independent variables. Let's say for the $k$th independent variable, the bivariate analysis shows a U-shaped trend - i.e., if I group $x_k$ into $20$ bins each containing roughly equal number of observations and calculate the 'bad rate' for each bin - # observations where y = 0 / total observations in each bin - then I get a U shaped curve.  My questions are:   Can I directly use $x_k$ as input while estimating the beta parameters? Are any statistical assumptions violated which might cause significant error in estimating the parameters? Is it necessary to 'linearize' this variable through a transformation (log, square, product with itself, etc.)? NetGear A6100 AC600 wireless adapter not working in Ubuntu 20.04. Worked fine in 18.04. Not same problem as previously Firstly, I know very well there are answers to this already. But, in my case, it is installed and shows in the terminal as such Bus 001 Device 007: ID 0846:9052 NetGear, Inc. A6100 AC600 DB Wireless Adapter [Realtek RTL8811AU]  It says it is installed in  as well.  I have tried downloading the driver for this adapter from several guides online, linking to GitHub, but no luck there either...  Any help is greatly appreciated! Thanks in advance!  EDIT: The answer from sudo dkms status command reads:  rtl8812au, 4.3.8.12175.20140902+dfsg, 5.4.0-31-generic, x86_64: installed  The other command  modinfo 8812au | grep 9052   spits out the following:  alias:          usb:v0846p9052d*dc*dsc*dp*ic*isc*ip*in* How can I optimise a Minecraft-esque voxel world? I found Minecraft's marvelous large worlds extremely slow to navigate, even with a quad core and meaty graphics card.  I assume Minecraft's slowness comes from:   Java, as spatial partitioning and memory management are faster in native C++. Weak world partitioning.   I could be wrong on both assumptions. However, this got me thinking about the best way to manage large voxel worlds. As it is a true 3D world, where a block can exist in any part of the world, it is basically a big 3D array [x][y][z], where each block in the world has a type (i.e BlockType.Empty = 0, BlockType.Dirt = 1, etc.)  I assume that to make this sort of world perform well, you would need to:   Use a tree of some variety (//) to split all the cubes out; it seems like an oct/kd would be the better option, as you can just partition on a per cube level not a per triangle level. Use some algorithm to work out which blocks can currently be seen, as blocks closer to the user could obfuscate the blocks behind, making it pointless to render them. Keep the block object themselves lightweight, so it is quick to add and remove them from the trees.   I guess there is no right answer to this, but I would be interested to see peoples' opinions on the subject.  How would you improve performance in a large voxel-based world? What do we mean by hyperparameters? Can anyone give me full details about what we mean by hyperparameters, and what in the Dirichlet distribution are called hyperparameters? A practice example for the estimation of those parameters would also be useful. How can I improve the performance of Minecraft?