Statistical inference using p-values results in accepting or rejecting a hypothesis given some p-value, say 0.05. So, if p = 0.05, we can conclude an effect is "significantly" different from zero with 95% confidence. However, I then test a second hypothesis with the same data set. Again, p = 0.05, and I can make the same claim. But wait, many statistical textbooks will preach that because its a second look at the data this p-value must be 'corrected' (read: penalized) to account for the fact that if you test enough hypotheses you will get positive results by random chance, even if nothing is truly happening. If you make 100 comparisons, 5 will erroneously detect an effect when none is present at a threshold of p = 0.05. To deal with this researchers perform a bonferroni correction, or apply the false discovery rate correction, or some other multiple-comparison correction method.  This does not make sense to me for two reasons:   The statement that an effect was detected at p=0.05 already communicates this information. Anyone who has been taught statistics should understand there is still some probability that the effect is spurrious, and the p-value communicates that probability.  The proposed correction methods guard against Type I errors (false positives), at the expense of artifically inflating the Type II error rate (false negatives). However, to my knowledge, there is no a priori reason why one error should be considered "worse" than the other. While some might argue that you want to be conservative in hypothesis testing and err on the side of caution, a far more effective strategy would be lowering your p-value threshold rather than ad hoc correcting your p-values.   All in all, a p-value is a pretty straightforward statistic. Its the probability a result may have been detected by chance. Its no more and no less than that. "Correcting" a p-value seems to do more harm than good in the context of interpretation.  Note: this is different than misunderstanding the  problem. I understand that if you run 20 tests, one will spuriously detect an effect (green jelly beans cause acne - though it should have been equally probable that some jelly bean color prevented acne...) What I do not understand is why multiple comparison corrections are an appropriate way to deal with this problem. The problem is always there.
I see that one time out of the twenty total tests they run, $p &lt; 0.05$, so they wrongly assume that during one of the twenty tests, the result is significant ($0.05 = 1/20$).      Title: Significant Hover text: "'So, uh, we did the green study again and got no link. It was probably a--' 'RESEARCH CONFLICTED ON GREEN JELLY BEAN/ACNE LINK; MORE STUDY RECOMMENDED!'"
Passing an enum value as command parameter from XAML I want to pass an enum value as command parameter in WPF, using something like this:  &lt;Button      x:Name="uxSearchButton"      Command="{Binding Path=SearchMembersCommand}"      CommandParameter="SearchPageType.First"     Content="Search"&gt; &lt;/Button&gt;   SearchPageType is an enum and this is to know from which button search command is invoked.  Is this possible in WPF, or how can you pass an enum value as command parameter? Is it possible to add multiple materials to a text object? I know that for a mesh you can go into edit mode and select vertices and assign a specific material to them quite easily. I want to know if it is possible to do this with a Text object (which has no vertices). Ubuntu 20.04 interface font too small after restart, even with high scaling factor So I was configuring VS code on my Notebook when suddenly I noticed that my interface font got really small on my desktop, terminal and files. I use Gnome Tweaks Tool to increase my scaling factor to 1,15 , but, even though it was active, the font stayed tiny. The solution I found was moving my scaling factor, which instantly fixed my font issue, however, every time I restart my Notebook the font gets tiny again and I have to repeat the process. I tried reseting my font configuration using this command, but had no success. gsettings reset org.gnome.desktop.interface text-scaling-factor  I also tried using the command dconf reset -f /  Finally, I tried using dconf-editor, but still had no success altering the font rendering DPI or changing the scaling factor. All of the steps I mentioned fixed my fonts temporarily, but the issue still persists when I restart my Notebook I am out of ideas and even considered getting a fresh Ubuntu install by now... My video card: NVIDIA GeForce GTX 1050 GPU I have been looking at the plugin API a bit more in depth recently and I was wondering what real differences there were between action and filter hooks. They both are events that receive data as a parameter and they seem to both be able to do the same things.  Obviously I see that actions are called when actions take place and filters are called when data is manipulated, but it seems to just be a semantic naming difference.  Besides semantics and what they are used for, what real differences are there between them? According to the microtype manual, Kerning, Spacing and Tracking are not enabled by default in pdftex (>= 1.4). What are the reasons for this? Inverse metric in linearised gravity From what I've read, in the framework of linearised gravity, one perturbs the metric around a Minkowski background, $\eta_{\mu\nu}$, such that  $$g_{\mu\nu}(x)=\eta_{\mu\nu}+h_{\mu\nu}(x)\tag{1}$$  where $h_{\mu\nu}(x)$ is a small perturbation, i.e. $$\big\lvert h_{\mu\nu}\big\rvert&lt;&lt;1.\tag{2}$$  The inverse metric is then found by assuming the following ansatz:  $$g^{\mu\nu}(x)=\eta^{\mu\nu}+\tilde{h}^{\mu\nu}\tag{3}$$  where $\tilde{h}^{\mu\nu}$ is also small (i.e. $\big\lvert \tilde{h}_{\mu\nu}\big\rvert&lt;&lt;1$).   Using this, it is easy to find that  $$g^{\mu\nu}(x)=\eta^{\mu\nu}-h^{\mu\nu} \tag{4}$$  to first order.   My question is, what is the justification for this ansatz? Is it simply that one expects the inverse metric to have a similar form to the metric in order to satisfy $$g^{\mu\alpha}g_{\alpha\nu}=\delta^{\mu}_{\;\nu}~?\tag{5}$$ Principled way of collapsing categorical variables with many levels? What techniques are available for collapsing (or pooling) many categories to a few, for the purpose of using them as an input (predictor) in a statistical model?    Consider a variable like  (discipline chosen by an undergraduate student). It is unordered and categorical, but it can potentially have dozens of distinct levels. Let's say I want to use major as a predictor in a regression model.  Using these levels as-is for modeling leads to all sorts of issues because there are just so many. A lot of statistical precision would be thrown away to use them, and the results are hard to interpret. We're rarely interested in specific majors -- we're much more likely to be interested in broad categories (subgroups) of majors. But it isn't always clear how to divide up the levels into such higher-level categories, or even how many higher-level categories to use.  For typical data I would be happy to use factor analysis, matrix factorization, or a discrete latent modeling technique. But majors are mutually exclusive categories, so I'm hesitant to exploit their covariance for anything.  Furthermore I don't care about the major categories on their own. I care about producing higher-level categories that are coherent with respect to my regression outcome. In the binary outcome case, that suggests to me something like linear discriminant analysis (LDA) to generate higher-level categories that maximize discriminative performance. But LDA is a limited technique and that feels like dirty data dredging to me. Moreover any continuous solution will be hard to interpret.  Meanwhile something based on covariances, like multiple correspondence analysis (MCA), seems suspect to me in this case because of the inherent dependence among mutually exclusive dummy variables -- they're better suited for studying multiple categorical variables, rather than multiple categories of the same variable.  edit: to be clear, this is about collapsing categories (not selecting them), and the categories are predictors or independent variables. In hindsight, this problem seems like an appropriate time to "regularize 'em all and let God sort 'em out". Glad to see this question is interesting to so many people! What does $b_i\mid b_{i+1}$ mean in this context? In the computational topology literature, the reduction algorithm for computing the Smith normal form of a boundary matrix uses the notation $b_j &gt; 1 \: \text{ and }\: b_j\mid b_{j+1}$ in the context of the diagonal elements of the Smith matrix. Can anyone give me an idea for what it means? find all $(x,y,z)$ such that $27^{3x^2 + 2y}+27^{3y^2 + 2z}+27^{3z^2 + 2x}=1$ Find all ($x,y,z$) such that $$ 27^{3x^2 + 2y}+27^{3y^2 + 2z}+27^{3z^2 + 2x}=1$$  I am a high school student and would appreciate it if anyone could solve it using high school mathematics. here is what I have tried till now: $$ 3x^2 +2y &lt; 0 $$ (this can also be said for the other 3 equation. it also means that x,y,z&lt;0) $$ -2y&gt;3x^2 $$ $$ 4y^2&gt;9x^2 $$ ( -2y and 3x^2 are both positive) $$ 3y^2&gt;27/4 x^2 $$ $$ -2z&gt;3y^2&gt;27/4 x^4 $$ $$ 4z^2 &gt; 729/16 x^8 $$ $$ 3z^2&gt; 2187/64 x^8 $$ $$ -128/2187&lt;x^7 $$ $$ -2/3 &lt; x $$ $$ -2/3&lt; x,y,z &lt; 0 $$ i tried this but as you can see didn't do much good Problem 4.3.32 in Linear Algebra, Lay:  Let $V$ and $W$ be vector spaces, let $T:V\to W$ be a linear transformation, and let $\{\mathbf{v}_1, \dots , \mathbf{v}_p \}$ be a subset of $V$. Suppose that $T$ is a one-to-one transformation [...]. Show that if the set of images $\{T(\mathbf{v}_1), \dots ,T(\mathbf{v}_p)\}$ is linearly dependent, then $\{\mathbf{v}_1, \dots , \mathbf{v}_p \}$ is linearly dependent. This fact shows that a one-to-one linear transformation maps a linearly independent set onto a linearly independent set.  All I can think of doing: If $\{T(\mathbf{v}_1), \dots ,T(\mathbf{v}_p)\}$ is linearly dependent, then there exist weights $c_1, \dots, c_p$, not all zero, so that $$c_1 T(\mathbf{v}_1) + \cdots + c_p T(\mathbf{v}_p) = \mathbf{0}$$ Since $T$ is linear: $$c_1 T(\mathbf{v}_1) + \cdots + c_p T(\mathbf{v}_p) = T(c_1\mathbf{v}_1) + \cdots + T(c_p \mathbf{v}_p)=T(c_1 \mathbf{v}_1 +\cdots + c_p \mathbf{v}_p)=\mathbf{0}$$ So the set $\{\mathbf{v}_1, \dots , \mathbf{v}_p \}$ must be linearly dependent. Am I missing something? And why must $T$ be on-to-one for this to be true? An example showing that it is not true if $T$ is not one-to-one would be great! Clearing all cookies with JavaScript Compute $\int\limits_{-\infty}^{\infty}\frac{1}{(1+x^2)^{n+1}}dx$ via residue calculus. Let $\Gamma_R$ be the semicircle of radius $R$ in the upper half plane. Then,  \begin{align} \int\limits_{-\infty}^{\infty}\frac{1}{(1+x^2)^{n+1}}dx  &amp;= \lim_{R\to \infty}\int_{\Gamma_R}\frac{1}{(1+z^2)^{n+1}}dz \\ &amp;= 2\pi i \operatorname{Res}\left(\frac{1}{(1+z^2)^{n+1}},i\right) \end{align} The pole of the function at $i$ is of order $n+1$, so the residue is computed by \begin{align} \operatorname{Res}\left(\frac{1}{(1+z^2)^{n+1}},i\right) &amp;= \frac{1}{n!}\lim_{z\to i}\frac{d^n}{dz^n}\left(\frac{1}{(z+i)^{n+1}}\right) \\ &amp;= \frac{1}{n!}\lim_{z\to i}(-1)^n\frac{(n+1)(n+2)\cdots(2n+1)}{(z+i)^{2n+1}} \\ &amp;=\frac{(2n+1)!}{i2^{2n+1}(n!)^2} \end{align} Hence, $$\int_{-\infty}^{\infty}\frac{1}{(1+x^2)^{n+1}}dx = \pi\frac{(2n+1)!}{2^{2n}(n!)^2}$$ The answer provided is $\frac{1\cdot 3\cdot 5\cdots(2n-1)}{2\cdot 4\cdot 6\cdots (2n)}\pi$. How do I manipulate my answer to obtain this answer? How do i fix this Eevee rendering Problem? I can notfix this issue when selecting Eevee for my renders. It gets really annoying. I can get rid of them temporary when I scroll out or into the viewport. Does anyone have an Idea how I can fix that?  thanks c: I have a large external with many subfolders that I want to move all videos, pictures, and music to another hard-drive, what would be the best way to do this? Truly destroying a PHP Session? Short Story: Army investigates barrier and house I am trying to identify the author and title of a short story with the following plot.  A scientist narrates a story where s/he is called in to help the army investigate an unexplained phenomena.  The army has cordoned off an area where a prairie home has appeared. It is surrounded by a dome that allows things to enter but not to leave. Briefing the scientist, the Army explains that it appears that it is a family of five with mother, father, son, daughter, and grandfather. They look completely normal and live an idyllic life of the 40s or 50s.  They continue to send probes in to investigate the dome and its proprieties. Not sure if this a time anomaly or another dimension.  An Army lieutenant, so enamored by their life runs through the barrier to join the family. The Family faces split into an unnaturally wide smile full of sharp teeth runs towards him and tears him to pieces &amp; eats him. The grandfather then looks up acts as if he can see the forces gathered outside the barrier. He then retrieves a book and it looks as if he reads it out loud and the house and barrier disappear. The narrator worries that the aliens will return. When an air-filled balloon is released without its opening tied up, it moves in a circular path rather than a straight line. Why is that? How to include third party Python libraries in Google App Engine? I am using wp_get_attachment_image_src to construct the srcset attribute of an img tag. In that attribute I want to output a comma separated list of image urls along with the image widths.  Using the Media Settings page, I have configured the image sizes to be as follows:   Thumbnail size: 150x150 Medium size: 640x480 Large size: 1024x768 Small size: 278x320   The wp_get_attachment_image_src function returns the correct urls and the correct widths for the image sizes full, medium and small. small is a custom size I added using add_image_size.  If I call wp_get_attachment_image_src( $image_id, 'large' ), the returned array looks like this:  array (     0 =&gt; 'http://localhost/wp-content/uploads/2014/10/image-1024x768.jpg',     1 =&gt; 640,     2 =&gt; 480,     3 =&gt; true, )   Checking the image which can be found at that url turns up the image with the correct dimensions.  Currently i am using the php builtin function  to circumvent this problem, but this function call takes significantly longer than simply accessing the index returned by wp_get_attachment_image_src:  Without getimagesize (mtime before and after execution):   '0.83761000 1415195440' '0.83831600 1415195440'   With getimagesize:   '0.34808000 1415195635'  '0.35323900 1415195635'   What can I do to make wp_get_attachment_image_src return the correct dimensions? Trying to find a book about kids with 'sunguns' revolting against alien overlords I'm trying to identify a book (or possibly a series, as I seem to recall reading a sequel which still left the story unfinished).  I read the book or books in the early 90's and had picked them up from a jumble sale at school, so they were probably published in the 80's or possibly 70's. I guess you would class them as YA fiction, though that wasn't really such a thing back then...  As I recall the story began with a slave transport craft crash landing on an alien world, with only a handful of teenage and pre-teen humans surviving. They scraped together what they could, including a couple of functional 'sunguns' (basically, laser rifles) and began a low level guerilla rebellion against the alien race that were using humanity as slave labour on the planet.  I've googled 'sungun' repeatedly, thinking that this should be the best way of finding the story but the references that come up are all for other stories or conspiracy technologies.  Anyone got any vague recollections of a book or series like this?